1. Let A be an m-by-n matrix. Let I be the n-by-n identity matrix. Explain why the matrix AI is identical to the matrix A. 2. If M is an n-by-n matrix, then the product of M with itself is also an...

1. Let A be an m-by-n matrix. Let I be the n-by-n identity matrix. Explain why the matrix AI is identical to the matrix A.

2. If M is an n-by-n matrix, then the product of M with itself is also an n-by-n matrix. We write matrix powers in the normal way that we defined powers of integers (or of the Cartesian product of sets): Mk = M M M, multiplied k times. (M0 is the n-by-n identity matrix I.) What are the following? (Hint: M²k = (Mk )
²
.)