Chapter 11.2, Problem 52E

To determine

(a)

To prove:

The expression ${\left(A+B\right)}^2=A^2+AB+BA+B^2$ when $A$ and $B$ are $2\times 2$ matrices.

To determine

(b)

Whether the expression ${\left(A+B\right)}^2\stackrel{?}{=}{A}^2+2AB+B^2$ is necessarily true when, $A$ and $B$ are $2\times 2$ matrices.