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# If Matrix A = $\begin{bmatrix} 3 &-3 \\ -3 & 3 \end{bmatrix}$, and $A^2=\lambda A$, then write the value of $\lambda$.

$A=\begin{bmatrix} 3 & -3 \\ -3 & 3 \end{bmatrix}\; and \;A^2=\lambda A$
$A^2=\begin{bmatrix} 3 & -3 \\ -3 & 3 \end{bmatrix}\; \begin{bmatrix} 3 & -3 \\ -3 & 3 \end{bmatrix}=\begin{bmatrix} 6 & -6 \\ -6 & 6 \end{bmatrix}$
$\;=2\;\begin{bmatrix} 3 & -3 \\ -3 & 3 \end{bmatrix}$
Therefore $\lambda =2$