# Compute the indicated matrices, if possible .A^2Blet A=begin{bmatrix}1 & 2 3 & 5 end{bmatrix} text{ and } B=begin{bmatrix}2 & 0 & -1 3 & -3 & 4 end{bmatrix}

Compute the indicated matrices, if possible .
${A}^{2}B$
let

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Step 1
Given:
$A=\left[\begin{array}{cc}1& 2\\ 3& 5\end{array}\right],B=\left[\begin{array}{ccc}2& 0& -1\\ 3& -3& 4\end{array}\right]$
To compute ${A}^{2}B$
Step 2
${A}^{2}=\left[\begin{array}{cc}1& 2\\ 3& 5\end{array}\right]\left[\begin{array}{cc}1& 2\\ 3& 5\end{array}\right]=\left[\begin{array}{cc}7& 12\\ 18& 31\end{array}\right]$
${A}^{2}B=\left[\begin{array}{cc}7& 12\\ 18& 31\end{array}\right]\left[\begin{array}{ccc}2& 0& -1\\ 3& -3& 4\end{array}\right]$
$=\left[\begin{array}{ccc}14+36& -36& -7+48\\ 36+93& -93& -18+124\end{array}\right]=\left[\begin{array}{ccc}50& -36& 41\\ 129& -93& 106\end{array}\right]$
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