Chapter 4.CE, Problem 1CE

CONCEPTUAL EXERCISES

In Exercises $1-8$, answer true or false. Justif your answer by providing a counterexample if the statement is false or an outline of a proof if the statement is true. In each exercises, A is a real $\left(n\times n\right)$ matrix.

If A is nonsingular with $A^{-1}=A^T$, then $\det \left(A\right)=1$