Chapter 2, Problem 6CTA

For each statement that follows, answer true if the statement is always true and false otherwise. In the case of a false statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is no always true. Assume that all the given matrices are $n\times n$ .

$\det \left(A^k\right)=\det {\left(A\right)}^k$