Question

If matrix $A=\left[\begin{array}{cc}2& -2\\ -2& 2\end{array}\right]$ and A² = pA, then write the value of p.

Answer 1

Given: $A=\left[\begin{array}{cc}2& -2\\ -2& 2\end{array}\right]$
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$$\begin{gathered} A^2=\left[\begin{array}{cc}2& -2\\ -2& 2\end{array}\right]\left[\begin{array}{cc}2& -2\\ -2& 2\end{array}\right] \\ =\left[\begin{array}{cc}4+4& -4-4\\ -4-4& 4+4\end{array}\right] \\ =\left[\begin{array}{cc}8& -8\\ -8& 8\end{array}\right] \\ =4\left[\begin{array}{cc}2& -2\\ -2& 2\end{array}\right] \\ =4A \end{gathered}$$

Hence, p = 4.