###### Exercise 7

Provide a justification for your response to the following questions.

Suppose that \(A\) is a square matrix with two identical columns. Can \(A\) be invertible?

Suppose that \(A\) is a square matrix with two identical rows. Can \(A\) be invertible?

Suppose that \(A\) is an invertible matrix and that \(AB = AC\text{.}\) Can you conclude that \(B = C\text{?}\)

Suppose that \(A\) is an invertible \(n\times n\) matrix. What can you say about the span of the columns of \(A^{-1}\text{?}\)

Suppose that \(A\) is an invertible matrix and that \(B\) is row equivalent to \(A\text{.}\) Can you guarantee that \(B\) is invertible?