 # compute the indicated matrices (I_2-D)^2 opatovaL 2021-01-28 Answered
compute the indicated matrices $\left({I}_{2}-D{\right)}^{2}$
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Step 1
Matrices:
$D=\left[\begin{array}{cc}0& -3\\ -2& 1\end{array}\right]$
${I}_{2}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
$\left({I}_{2}-D{\right)}^{2}$
$={\left(\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]-\left[\begin{array}{cc}0& -3\\ -2& 1\end{array}\right]\right)}^{2}$
$={\left[\begin{array}{cc}1& 3\\ 2& 0\end{array}\right]}^{2}$
Step 2
$=\left[\begin{array}{cc}1& 3\\ 2& 0\end{array}\right]\left[\begin{array}{cc}1& 3\\ 2& 0\end{array}\right]$
$=\left[\begin{array}{cc}1\cdot 1+3\cdot 2& 1\cdot 3\\ 2\cdot 1+0\cdot 2& 2\cdot 3\end{array}\right]$
$=\left[\begin{array}{cc}7& 3\\ 2& 6\end{array}\right]$
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