Question
Given $A=\left[\begin{array}{ll}4 & 1 \\ 2 & 3\end{array}\right]$ and $B=\left[\begin{array}{cc}1 & 0 \\ -2 & 1\end{array}\right]$ Find $A^2-A B+2 B$
✓
Answer
$A^2-A B+2 B$
$\begin{array}{l}=\left[\begin{array}{cc}18 & 7 \\ 14 & 11\end{array}\right]-\left[\begin{array}{cc}2 & 1 \\ -4 & 3\end{array}\right]+2\left[\begin{array}{cc}1 & 0 \\ -2 & 1\end{array}\right] \end{array} $
$ =\left[\begin{array}{cc}16 & 6 \\ 18 & 8\end{array}\right]+\left[\begin{array}{cc}2 & 0 \\ -4 & 2\end{array}\right] $
$ =\left[\begin{array}{cc}18 & 6 \\ 14 & 10\end{array}\right]$
$\begin{array}{l}=\left[\begin{array}{cc}18 & 7 \\ 14 & 11\end{array}\right]-\left[\begin{array}{cc}2 & 1 \\ -4 & 3\end{array}\right]+2\left[\begin{array}{cc}1 & 0 \\ -2 & 1\end{array}\right] \end{array} $
$ =\left[\begin{array}{cc}16 & 6 \\ 18 & 8\end{array}\right]+\left[\begin{array}{cc}2 & 0 \\ -4 & 2\end{array}\right] $
$ =\left[\begin{array}{cc}18 & 6 \\ 14 & 10\end{array}\right]$
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