If  A=2−1−13  evaluate A2−3A+2I, where  Iis a unit matrix of order “2”

If  $A=\left[\begin{array}{ll}2& -1\\ -1& 3\end{array}\right]$  evaluate ${A}^{2}-3A+2I$, where  $I$is a unit matrix of order “2”

1. A

$\left[\begin{array}{ll}1& -2\\ 3& -2\end{array}\right]$

2. B

$\left[\begin{array}{ll}1& 3\\ 4& 5\end{array}\right]$

3. C

$\left[\begin{array}{ll}1& -2\\ -2& 3\end{array}\right]$

4. D

$\left[\begin{array}{ll}3& -2\\ -2& 1\end{array}\right]$

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Solution:

$\begin{array}{l}={A}^{2}-3A+2I\\ =\left[\begin{array}{ll}2& -1\\ -1& 3\end{array}\right].\left[\begin{array}{ll}2& -1\\ -1& 3\end{array}\right]-3\left[\begin{array}{ll}2& -1\\ -1& 3\end{array}\right]+2\left[\begin{array}{ll}1& 0\\ 0& 1\end{array}\right]\\ =\left[\begin{array}{ll}5& -5\\ -5& 10\end{array}\right]-\left[\begin{array}{ll}6& -3\\ -3& 9\end{array}\right]+\left[\begin{array}{ll}2& 0\\ 0& 2\end{array}\right]\\ =\left[\begin{array}{ll}1& -2\\ -2& 3\end{array}\right]\end{array}$

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