Solve each problem and simplify it with no variables A=[a−213],B=[4−5b7] what is A+B2? What is...

Step 1
We have to find the matrix
$A=\left[\begin{array}{cc}a& -2\\ 1& 3\end{array}\right],B=\left[\begin{array}{cc}4& -5\\ b& 7\end{array}\right]$
$A^2=\left[\begin{array}{cc}a& -2\\ 1& 3\end{array}\right]\left[\begin{array}{cc}a& -2\\ 1& 3\end{array}\right]$
$=\left[\begin{array}{cc}{a}^2-2& -2a-6\\ a+3& -2+9\end{array}\right]=\left[\begin{array}{cc}{a}^2-2& -2a-6\\ a+3& 7\end{array}\right]$
$A^2-B=\left[\begin{array}{cc}{a}^2-2& -2a-6\\ a+3& 7\end{array}\right]-\left[\begin{array}{cc}4& -5\\ b& 7\end{array}\right]$
$=\left[\begin{array}{cc}{a}^2-6& -2a-1\\ a+3-b& 0\end{array}\right]$
$B^2=\left[\begin{array}{cc}4& -5\\ b& 7\end{array}\right]\left[\begin{array}{cc}4& -5\\ b& 7\end{array}\right]$
$=\left[\begin{array}{cc}16-5b& -20-35\\ 4b+7b& -5b+49\end{array}\right]$
$A+B^2=\left[\begin{array}{cc}a+16-5b& -57\\ 11b+1& -5b+52\end{array}\right]$
$A+B^2=\left[\begin{array}{cc}a+16-5b& -57\\ 11b+1& -5b+52\end{array}\right]$