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Question
If matrix \[A = \begin{bmatrix}2 & - 2 \\ - 2 & 2\end{bmatrix}\] and A2 = pA, then write the value of p.
Solution
\[A^2 = \begin{bmatrix}2 & - 2 \\ - 2 & 2\end{bmatrix}\begin{bmatrix}2 & - 2 \\ - 2 & 2\end{bmatrix}\]
\[ = \begin{bmatrix}4 + 4 & - 4 - 4 \\ - 4 - 4 & 4 + 4\end{bmatrix}\]
\[ = \begin{bmatrix}8 & - 8 \\ - 8 & 8\end{bmatrix}\]
\[ = 4\begin{bmatrix}2 & - 2 \\ - 2 & 2\end{bmatrix}\]
\[ = 4A\]
Hence, p = 4.
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