[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-18, -1, -16, -6, -9, 13, -19, 20, -15],
 [0, -14, -5, 24, 10, 16, -15, -12, -16],
 [0, 0, -22, 21, -23, 0, 13, 10, -21],
 [0, 0, 0, -2, 12, 6, 0, 1, -3],
 [0, 0, 0, 0, 9, 10, 16, -7, -20],
 [0, 0, 0, 0, 0, 9, 7, 11, 25],
 [0, 0, 0, 0, 0, 0, 1, -8, -4],
 [0, 0, 0, 0, 0, 0, 0, 15, -18],
 [0, 0, 0, 0, 0, 0, 0, 0, -9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-4, 4, -8, -2, -18, -15, 5, -18, -6],
 [4, -1, 1, 10, -7, -10, -6, 4, -10],
 [-8, 1, -17, -16, 2, -14, 6, 1, 13],
 [-2, 10, -16, 14, -9, 7, -13, 20, 12],
 [-18, -7, 2, -9, -23, 2, 0, -8, 9],
 [-15, -10, -14, 7, 2, -17, 8, 3, -7],
 [5, -6, 6, -13, 0, 8, -24, 0, 12],
 [-18, 4, 1, 20, -8, 3, 0, 11, -19],
 [-6, -10, 13, 12, 9, -7, 12, -19, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-7, -18, 10, -22, -6, 13, 9, 6, -6],
 [-18, 12, -10, -15, 6, 22, -10, -4, -11],
 [10, -10, 3, -6, 13, 1, -21, 12, 10],
 [-22, -15, -6, 16, -3, 2, -2, -4, -12],
 [-6, 6, 13, -3, -19, -10, -5, -9, 8],
 [13, 22, 1, 2, -10, 17, -8, 18, 9],
 [9, -10, -21, -2, -5, -8, -3, 10, 4],
 [6, -4, 12, -4, -9, 18, 10, 16, 11],
 [-6, -11, 10, -12, 8, 9, 4, 11, 2]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-10, 19, -17, -14, -3, 15, 9, -8, 20],
 [0, 4, 4, 10, 9, 7, 16, 6, 2],
 [0, 0, -11, 16, 18, -2, 6, 25, -24],
 [0, 0, 0, 15, 21, 11, -6, -15, 3],
 [0, 0, 0, 0, -9, 13, -11, 22, -2],
 [0, 0, 0, 0, 0, -5, 4, 7, -14],
 [0, 0, 0, 0, 0, 0, -5, 25, 21],
 [0, 0, 0, 0, 0, 0, 0, 9, -20],
 [0, 0, 0, 0, 0, 0, 0, 0, 4]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-22, -22, -5, -2, -25, 7, -1, 7, 12],
 [0, -5, -5, -3, -7, 6, -15, -10, 5],
 [0, 0, -4, 15, 11, -11, 12, 6, -8],
 [0, 0, 0, -21, -16, 3, -8, -2, 2],
 [0, 0, 0, 0, 21, -17, -7, -16, 7],
 [0, 0, 0, 0, 0, -23, -6, 9, 11],
 [0, 0, 0, 0, 0, 0, 11, -8, -3],
 [0, 0, 0, 0, 0, 0, 0, -15, 3],
 [0, 0, 0, 0, 0, 0, 0, 0, 9]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-4, 7, 13, -4, 2, -23, -15, 8, -21],
 [1, -12, -14, -17, 16, 5, -13, 16, -21],
 [-17, 22, 24, -21, -8, 5, -4, -23, 12],
 [12, -7, -13, 21, 12, -10, -8, 4, 12],
 [13, -9, -21, 18, 2, 0, 9, -15, -14],
 [-2, -15, -3, -2, 14, -12, -16, 7, 25],
 [9, -18, 6, 21, -1, 12, -7, 4, -8],
 [12, 13, 22, -19, -21, -4, -11, 20, 19],
 [-18, -9, -12, 17, 8, -1, 23, 18, -11]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the value of det(A) where A =
[[-21, -8, -18, -21, 10, -6, 0, -16, 6],
 [-8, -12, 0, -14, 2, 8, -2, -19, 7],
 [-18, 0, 9, 8, 1, -5, -4, -18, -8],
 [-21, -14, 8, 9, -2, -6, -9, 11, 2],
 [10, 2, 1, -2, -16, 12, 0, -19, -9],
 [-6, 8, -5, -6, 12, -17, 0, 0, 12],
 [0, -2, -4, -9, 0, 0, 24, 24, 8],
 [-16, -19, -18, 11, -19, 0, 24, 3, 0],
 [6, 7, -8, 2, -9, 12, 8, 0, -10]]
Round to the nearest integer, then give your answer as det(A) mod 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[16, -15, 9, -1, -5, -4, 8, 2, 22],
 [-15, 23, 3, 10, -19, 18, -6, 7, -22],
 [9, 3, 19, 14, -5, 10, -10, -4, 0],
 [-1, 10, 14, 24, 0, 4, -8, -12, -8],
 [-5, -19, -5, 0, 22, 8, 6, -2, 9],
 [-4, 18, 10, 4, 8, 14, -10, 12, 6],
 [8, -6, -10, -8, 6, -10, -5, 4, 8],
 [2, 7, -4, -12, -2, 12, 4, -22, 0],
 [22, -22, 0, -8, 9, 6, 8, 0, 14]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[15, 11, -13, -6, 20, 25, 17, -10, -15],
 [0, -25, 7, -18, 14, 15, -19, 15, -19],
 [0, 0, -6, -1, -5, 21, -3, -16, 15],
 [0, 0, 0, 15, 4, 7, -18, 23, 14],
 [0, 0, 0, 0, 4, -21, 19, -18, 5],
 [0, 0, 0, 0, 0, 16, -8, 25, -15],
 [0, 0, 0, 0, 0, 0, -22, -19, -5],
 [0, 0, 0, 0, 0, 0, 0, -15, 14],
 [0, 0, 0, 0, 0, 0, 0, 0, -1]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[9, -8, -6, -7, -14, 24, -3, -19, -14],
 [0, -2, 20, 17, 5, 15, -24, -22, 1],
 [0, 0, -6, -14, 17, 14, -4, -3, -14],
 [0, 0, 0, -20, 0, 6, 4, 13, 20],
 [0, 0, 0, 0, 9, -15, 11, -17, 24],
 [0, 0, 0, 0, 0, 4, -22, -3, 11],
 [0, 0, 0, 0, 0, 0, 2, 15, 6],
 [0, 0, 0, 0, 0, 0, 0, -20, -3],
 [0, 0, 0, 0, 0, 0, 0, 0, 23]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[6, -10, -21, -21, -10, -6, -19, 8, 4],
 [0, 16, -3, 19, 15, -7, -20, -9, -6],
 [0, 0, 23, 13, -5, -8, 13, 14, -9],
 [0, 0, 0, 9, 22, 3, -2, -14, 17],
 [0, 0, 0, 0, -22, -3, 1, -11, -8],
 [0, 0, 0, 0, 0, 14, 25, 1, -25],
 [0, 0, 0, 0, 0, 0, -4, -1, -21],
 [0, 0, 0, 0, 0, 0, 0, -11, 23],
 [0, 0, 0, 0, 0, 0, 0, 0, 9]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[12, -1, -15, 4, -22, 6, 0, -2, -19],
 [-12, -20, -9, 10, -14, -14, -15, -4, 20],
 [20, -19, -2, 11, -8, 0, 22, 3, 15],
 [-20, 7, 5, 22, -17, 15, 16, 7, 25],
 [18, -25, 4, 8, 25, -25, 13, -14, 14],
 [-5, 18, 18, 11, 18, 24, -5, 13, -12],
 [-11, 15, -19, 15, -18, -17, -5, -17, -22],
 [16, -3, -4, 3, 22, -10, -3, 12, -20],
 [-1, -3, 4, 11, 13, 5, 15, -16, 18]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-22, 22, 14, -23, 7, -15, -11, 0, -7],
 [0, -3, -6, 22, 24, -11, 7, 11, -23],
 [0, 0, -18, 11, 5, -6, -10, 4, 8],
 [0, 0, 0, -1, 11, -6, -7, 6, 23],
 [0, 0, 0, 0, 6, -21, 1, 2, -17],
 [0, 0, 0, 0, 0, -3, 4, 13, -8],
 [0, 0, 0, 0, 0, 0, 1, -4, 4],
 [0, 0, 0, 0, 0, 0, 0, -16, 16],
 [0, 0, 0, 0, 0, 0, 0, 0, 25]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[11, -14, -22, -16, -10, 11, 20, 19, 8],
 [-17, 14, -17, 17, -18, 12, -24, 1, -6],
 [-20, 17, 9, -15, 6, -15, -1, -24, -13],
 [20, 11, -1, 11, 3, -10, 5, -23, 14],
 [-14, 21, -9, -9, -14, 9, 7, 23, 1],
 [7, 22, 23, -11, -14, 4, 11, 1, -5],
 [-23, -13, -4, -18, -15, -8, 18, -9, 21],
 [-24, -20, -16, -7, -17, -14, 6, 0, -19],
 [9, 8, 11, -23, 9, 17, 13, -1, -6]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[-9, -16, -25, 8, 17, 9, -15, -14, 1],
 [3, 25, 25, -25, 8, -6, 20, 5, -25],
 [-10, -22, -4, 10, -17, 17, 24, -17, -21],
 [-10, -6, 3, -25, -9, 9, 24, -14, -15],
 [24, 10, -2, 23, 16, -13, 13, -23, 20],
 [24, -2, -25, 12, -18, 7, 20, 19, -5],
 [25, 22, 3, -16, -5, 9, 9, 18, -17],
 [-6, -22, 21, 17, -16, -6, 5, -8, 5],
 [11, 5, 17, -6, 16, 11, -12, -20, -23]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[2, 0, 21, -17, -9, 20, 7, 20, 17],
 [14, -10, -10, -23, 20, 4, -22, 0, 24],
 [-10, -7, -25, 20, 13, -25, -9, 7, -3],
 [23, 7, 6, -24, -1, 1, 24, 17, -6],
 [16, -11, 12, 24, -4, 5, -18, 25, -12],
 [10, -13, 6, 1, 19, -1, 22, 1, -20],
 [-19, 8, -22, 16, 12, -9, -12, 19, 6],
 [5, 8, -14, -17, 3, -11, 17, 6, -24],
 [23, 4, 17, -15, 25, -9, -15, 2, 15]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[17, 11, -4, -2, -2, 4, 17, -17, 8],
 [11, 18, 14, 5, 6, 7, 4, -12, -18],
 [-4, 14, -12, 9, 4, 0, 8, 2, 8],
 [-2, 5, 9, 22, -2, -4, -3, 14, -2],
 [-2, 6, 4, -2, 20, 10, -8, 4, 6],
 [4, 7, 0, -4, 10, 5, -10, 7, -16],
 [17, 4, 8, -3, -8, -10, 25, 10, 4],
 [-17, -12, 2, 14, 4, 7, 10, 20, 2],
 [8, -18, 8, -2, 6, -16, 4, 2, 23]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[3, 8, -9, -10, 17, -12, -10, 21, -21],
 [0, 11, 24, 12, 0, -7, -16, -22, 12],
 [0, 0, 14, 16, -9, -23, 14, -16, 19],
 [0, 0, 0, -10, -20, 1, -25, 7, 17],
 [0, 0, 0, 0, -11, -2, -2, 16, -20],
 [0, 0, 0, 0, 0, -22, -14, -13, 20],
 [0, 0, 0, 0, 0, 0, -6, 2, 25],
 [0, 0, 0, 0, 0, 0, 0, -10, 22],
 [0, 0, 0, 0, 0, 0, 0, 0, 23]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[6, 18, 13, -24, 13, -1, 25, -23, 17],
 [0, 14, 5, -6, 6, 23, 19, 8, 0],
 [0, 0, 16, 16, 12, -14, -10, -20, -22],
 [0, 0, 0, -2, -10, -7, 2, 14, -6],
 [0, 0, 0, 0, 9, -24, 23, 9, -16],
 [0, 0, 0, 0, 0, 20, 7, 22, -24],
 [0, 0, 0, 0, 0, 0, -23, -16, 4],
 [0, 0, 0, 0, 0, 0, 0, -13, 24],
 [0, 0, 0, 0, 0, 0, 0, 0, 22]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[4, 14, -16, 12, 0, -4, 21, -15, 10],
 [14, 14, -4, 10, -18, 8, -8, 8, 14],
 [-16, -4, -16, -14, 4, -18, -20, -1, -18],
 [12, 10, -14, 21, -12, -18, -3, -2, 0],
 [0, -18, 4, -12, -2, -4, 5, -17, 14],
 [-4, 8, -18, -18, -4, 18, -4, 12, 10],
 [21, -8, -20, -3, 5, -4, -15, -8, -11],
 [-15, 8, -1, -2, -17, 12, -8, 12, 22],
 [10, 14, -18, 0, 14, 10, -11, 22, -20]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the determinant of the following matrix. Round to the nearest integer, then give your answer modulo 1000:
[[-21, -16, 15, -18, -4, -19, 25, -4, -15],
 [0, 25, -11, -20, 12, 10, 13, 11, 11],
 [0, 0, -3, -13, -22, 23, 18, -2, -11],
 [0, 0, 0, -10, -8, 15, -5, 13, 24],
 [0, 0, 0, 0, 24, 24, 19, 3, -15],
 [0, 0, 0, 0, 0, -24, 4, 14, -5],
 [0, 0, 0, 0, 0, 0, -22, 18, 4],
 [0, 0, 0, 0, 0, 0, 0, -15, 19],
 [0, 0, 0, 0, 0, 0, 0, 0, -24]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[3, 12, -2, 0, -20, -13, -18, -2, -5],
 [12, -9, -4, -7, 1, 10, 13, -8, -5],
 [-2, -4, 16, 0, -8, 6, -4, 8, 0],
 [0, -7, 0, -12, -17, -10, -14, -16, 7],
 [-20, 1, -8, -17, -19, 12, -6, 13, 8],
 [-13, 10, 6, -10, 12, 4, 2, -18, -6],
 [-18, 13, -4, -14, -6, 2, -18, 6, 2],
 [-2, -8, 8, -16, 13, -18, 6, 4, 6],
 [-5, -5, 0, 7, 8, -6, 2, 6, 20]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-10, -8, 24, 10, -8, 8, 21, 12, -11],
 [-12, -3, -6, 21, -13, 1, -25, -20, -4],
 [-11, -25, 9, -3, -20, 18, 21, 5, -25],
 [-9, -9, -18, 12, -22, 24, 4, -7, -20],
 [11, -3, -22, 4, 22, -8, 11, -8, -5],
 [8, 10, -4, 3, -21, 8, 23, -9, -19],
 [-17, 10, 24, -24, -19, 8, 3, -20, 5],
 [0, -15, -7, -4, -20, -7, -18, -5, -14],
 [-9, -1, -13, -25, 1, 6, -3, 8, -11]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Calculate the determinant of the matrix, round to the nearest integer, then find the result modulo 1000:
[[4, -4, -4, -4, -8, 4, -14, 11, 22],
 [-4, -13, 22, 0, 2, -4, 2, 12, 8],
 [-4, 22, -19, -16, 0, -12, -9, 16, 20],
 [-4, 0, -16, -1, -16, -9, 4, 8, 16],
 [-8, 2, 0, -16, -24, -10, 16, 14, -18],
 [4, -4, -12, -9, -10, 4, -17, 6, 8],
 [-14, 2, -9, 4, 16, -17, 11, 5, 4],
 [11, 12, 16, 8, 14, 6, 5, -15, 10],
 [22, 8, 20, 16, -18, 8, 4, 10, 8]]

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[-7, -16, 18, -1, 15, 6, 0, -12, -14],
 [-16, 16, -2, -2, 4, -4, -8, 2, -6],
 [18, -2, -4, 8, 8, 8, 4, 18, 18],
 [-1, -2, 8, 4, 6, 8, 0, -3, 16],
 [15, 4, 8, 6, 16, 14, -8, -8, 9],
 [6, -4, 8, 8, 14, -7, 18, -2, 4],
 [0, -8, 4, 0, -8, 18, 19, 11, 7],
 [-12, 2, 18, -3, -8, -2, 11, -5, 0],
 [-14, -6, 18, 16, 9, 4, 7, 0, 23]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[7, -18, 2, -10, 0, -6, -8, 8, -9],
 [-18, -21, 9, 2, -14, 18, -10, 1, -18],
 [2, 9, -1, 1, -8, 13, -4, 6, 2],
 [-10, 2, 1, -8, -16, -15, 10, 2, 8],
 [0, -14, -8, -16, -4, 6, -18, 5, -2],
 [-6, 18, 13, -15, 6, -21, 8, -1, 13],
 [-8, -10, -4, 10, -18, 8, 25, 10, 3],
 [8, 1, 6, 2, 5, -1, 10, -16, 7],
 [-9, -18, 2, 8, -2, 13, 3, 7, 6]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Compute |A| for the matrix A =
[[-12, 3, -18, -4, -15, -2, -4, -2, -6],
 [3, -11, -11, 16, -4, 20, -17, -12, 11],
 [-18, -11, -5, -2, 12, 8, -12, 11, -12],
 [-4, 16, -2, 19, 18, -18, 10, 8, 4],
 [-15, -4, 12, 18, -14, 0, 3, -8, 4],
 [-2, 20, 8, -18, 0, -12, -10, -4, -5],
 [-4, -17, -12, 10, 3, -10, -9, -13, 2],
 [-2, -12, 11, 8, -8, -4, -13, -12, 12],
 [-6, 11, -12, 4, 4, -5, 2, 12, -14]]
Round to the nearest integer, then take the result modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}


[User]
What is the determinant of the matrix:
[[21, -3, -14, -10, 19, -1, 20, -21, -11],
 [11, 9, -6, -19, 10, -13, 15, 25, 6],
 [18, -20, -19, 9, 11, -4, 19, -12, -21],
 [-2, -10, 15, -22, 22, 21, 23, -7, 15],
 [13, 10, -14, 21, -4, 4, 13, -15, 10],
 [-2, -9, -9, -15, -10, -18, 3, 21, 0],
 [-3, -14, -9, -14, -21, -8, -2, 8, -21],
 [25, 25, -7, 11, 5, -20, 18, 9, -25],
 [6, 23, -18, 22, 16, -14, 0, -10, 6]]? Round to the nearest integer, then express your answer modulo 1000.

Present the answer in LaTex format: \boxed{Your answer}