Chapter 2.2, Problem 10E

a. A product of invertible n × n matrices is invertible, and the inverse of the product is the product of their inverses in the same order.

b. If A is invertible, then the inverse of A⁻¹ is A itself.

c. If A = $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ and ad = bc. then A is not invertible.

d. If A can be row reduced to the identity matrix, then A must be invertible.

e. If A is invertible, then elementary row operations that reduce A to the identity I_n also reduce A⁻¹ to I_n.