Question
If $A=\left[\begin{array}{cc}0 & 2 \\ 5 & -2\end{array}\right], B=\left[\begin{array}{cc}1 & -1 \\ 3 & 2\end{array}\right]$ and $I$ is a unit matrix of order $2 \times 2.$ Find $AI.$
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Answer
$\begin{array}{l}A I=\left[\begin{array}{cc}0 & 2 \\ 5 & -2\end{array}\right]\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \end{array} $
$ =\left[\begin{array}{cc}0(1)+2(0) & 0(0)+(2)(1) \\ 5(1)+(-2)(0) & (5)(0)+(-2)(1)\end{array}\right] $
$ =\left[\begin{array}{cc}0+0 & 0+2 \\ 5+0 & 0-2\end{array}\right] $
$ =\left[\begin{array}{cc}0 & 2 \\ 5 & -2\end{array}\right]$
$ =\left[\begin{array}{cc}0(1)+2(0) & 0(0)+(2)(1) \\ 5(1)+(-2)(0) & (5)(0)+(-2)(1)\end{array}\right] $
$ =\left[\begin{array}{cc}0+0 & 0+2 \\ 5+0 & 0-2\end{array}\right] $
$ =\left[\begin{array}{cc}0 & 2 \\ 5 & -2\end{array}\right]$
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