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Question
If matrix \[A = \left[ a_{ij} \right]_{2 \times 2}\] where
Options
I
A
O
-I
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Solution
Given:
\[\therefore a_{11} = 0\]
\[ a_{12} = 1\]
\[ a_{21} = 1\]
\[ a_{22} = 0\]
\[\text{Therefore}, matrix A = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}\]
\[ A^2 = \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}\]
\[ = \begin{bmatrix}0 + 1 & 0 + 0 \\ 0 + 0 & 1 + 0\end{bmatrix}\]
\[ = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\]
= I
Hence, the correct option is (a).
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