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Question
If \[A = \begin{bmatrix}i & 0 \\ 0 & i\end{bmatrix}\] , write A2.
Sum
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Solution
\[Given: A = \begin{bmatrix}i & 0 \\ 0 & i\end{bmatrix}\]
\[ A^2 = AA\]
\[ \Rightarrow A^2 = \begin{bmatrix}i & 0 \\ 0 & i\end{bmatrix}\begin{bmatrix}i & 0 \\ 0 & i\end{bmatrix}\]
\[ \Rightarrow A^2 = \begin{bmatrix}i^2 + 0 & 0 + 0 \\ 0 + 0 & 0 + i^2\end{bmatrix}\]
\[ \Rightarrow A^2 = \begin{bmatrix}i^2 & 0 \\ 0 & i^2\end{bmatrix}\]
\[ \Rightarrow A^2 = \begin{bmatrix}- 1 & 0 \\ 0 & - 1\end{bmatrix} \left( \because i^2 = - 1 \right)\]
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