Question: In this problem, we consider another important type of matrices which is called an inverse matrix. An inverse matrix B of an nn matrix A

In this problem, we consider another important type of matrices which is called an inverse matrix. An inverse matrix B of an nn matrix A is a matrix which satisfies BA = AB = I_n () where I_n is the identity matrix of size n n. We call a matrix A invertible if there exists an inverse matrix of A

(1) Suppose that A is invertible, and B and C are inverse matrices of A. Prove that B = C

(2) Suppose that A is invertible. Prove that A^t is also invertible by giving its inverse matrix, and showing the matrix you found satisfies the condition ()

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