Exercise7

Suppose that \(A\) and \(B\) are \(n\times n\) matrices.

  1. If \(A\) and \(B\) are both invertible, use determinants to explain why \(AB\) is invertible.

  2. If \(AB\) is invertible, use determinants to explain why both \(A\) and \(B\) is invertible.

in-context