Find A2
Given:
\[ A = \begin{bmatrix} i & 0 \\ 0 & i \end{bmatrix} \]
Step 1: Compute A2 = A × A
\[ A^2 = \begin{bmatrix} i & 0 \\ 0 & i \end{bmatrix} \begin{bmatrix} i & 0 \\ 0 & i \end{bmatrix} \]
\[ A^2 = \begin{bmatrix} i \cdot i + 0 \cdot 0 & i \cdot 0 + 0 \cdot i \\ 0 \cdot i + i \cdot 0 & 0 \cdot 0 + i \cdot i \end{bmatrix} \]
Step 2: Use \(i^2 = -1\)
\[ A^2 = \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix} \]
Final Answer:
\[ A^2 = \begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix} \]