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  4. If A = [2&-1 -1&2] and I is the unit matrix of order 2, then A2 is equal to

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Q. If $A = \begin{bmatrix}2&-1\\ -1&2\end{bmatrix} $ and $I$ is the unit matrix of order 2, then $A^2$ is equal to

Matrices

Solution:

$A^{2} = AA = \begin{bmatrix}2&-1\\ -1&2\end{bmatrix} \begin{bmatrix}2&-1\\ -1&2\end{bmatrix} $
$= \begin{bmatrix}5&-4\\ -4&5\end{bmatrix}=\begin{bmatrix}8&-4\\ -4&8\end{bmatrix} - \begin{bmatrix}3&0\\ 0&3\end{bmatrix}$
$= 4 A - 3 I$