Question
If $A=\left[\begin{array}{cc}1 & -2 \\ 5 & 6\end{array}\right], B=\left[\begin{array}{cc}3 & -1 \\ 3 & 7\end{array}\right]$, find $A B-2 l_t$ where $\mathrm{I}$ is unit matrix of order 2 .

Answer

$A B-2 I=\left[\begin{array}{cc}1 & -2 \\ 5 & 6\end{array}\right]\left[\begin{array}{cc}3 & -1 \\ 3 & 7\end{array}\right]-2\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$

$\begin{aligned} & =\left[\begin{array}{cc}3-6 & -1-14 \\ 15+18 & -5+42\end{array}\right]-\left[\begin{array}{ll}2 & 0 \\ 0 & 2\end{array}\right] \\ & =\left[\begin{array}{cc}-3 & -15 \\ 33 & 37\end{array}\right]-\left[\begin{array}{ll}2 & 0 \\ 0 & 2\end{array}\right] \\ & =\left[\begin{array}{cc}-3-2 & -15-0 \\ 33-0 & 37-2\end{array}\right] \\ & =\left[\begin{array}{cc}-5 & -15 \\ 33 & 35\end{array}\right]\end{aligned}$

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