Answer
$a.$
$(A+B)(A+B)=\qquad$ apply distribution
$(A+B)A+(A+B)B=\qquad$ apply distribution
$AA+BA+AB+BB=A^{2}+BA+AB+B^{2}$
$ b.\qquad$No
Work Step by Step
$a.$
$(A+B)(A+B)=\qquad$ apply distribution
$(A+B)A+(A+B)B=\qquad$ apply distribution
$AA+BA+AB+BB=A^{2}+BA+AB+B^{2}$
$b.$
Since multiplication of matrices is not commutative,
in general we will have $AB\neq BA.$
Thus, we cannot say $BA+AB=2AB$, so
the statement is not true.
