Question: Let A be a matrix with the following elements: A = [1, 2, 3; 4, 5, 6; 7, 8, 9] Prove that det(A^3) = (det(A))^3

Let A be a matrix with the following elements:
A = [1, 2, 3; 4, 5, 6; 7, 8, 9]
Prove that det(A^3) = (det(A))^3
where det(A) is the determinant of matrix A and A^3 is the matrix A multiplied by itself 3 times.

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