Question: Construct a random integer-valued 4 4 matrix A, and verify that A and A T have the same characteristic polynomial (the same eigenvalues with

Construct a random integer-valued 4 × 4 matrix A, and verify that A and A^T have the same characteristic polynomial (the same eigenvalues with the same multiplicities). Do A and A^T have the same eigenvectors? Make the same analysis of a 5 × 5 matrix. Report the matrices and your conclusions.

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