Question

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

 

Answer 1

Given: 

\[A = \begin{bmatrix}2 & - 2 \\ - 2 & 2\end{bmatrix}\]

\[A^2 = \begin{bmatrix}2 & - 2 \\ - 2 & 2\end{bmatrix}\begin{bmatrix}2 & - 2 \\ - 2 & 2\end{bmatrix}\]

\[ = \begin{bmatrix}4 + 4 & - 4 - 4 \\ - 4 - 4 & 4 + 4\end{bmatrix}\]

\[ = \begin{bmatrix}8 & - 8 \\ - 8 & 8\end{bmatrix}\]

\[ = 4\begin{bmatrix}2 & - 2 \\ - 2 & 2\end{bmatrix}\]

\[ = 4A\]

Hence, p = 4.