Chapter 2.3, Problem 72E

True or False ? In Exercises 71 and 72, determine whether each statement is true or false. If a statement is true or false. If a statement is true, give a reason or cite an appropriaste statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.

(a) The inverse of the inverse of a non-singular matrix $A$, ${\left(A^{-1}\right)}^{-1}$, is equal to $A$ itself.

(b) The matrix $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ is invertible when $ab-dc\ne 0$.

(c) If $A$ is a square matrix, then the system of linear equations $A\mathbf{x}=\mathbf{b}$ has a unique solution.