If $A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$, then $A^2$ is equal to:
(a) $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$
(b) $\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$
(c) $\begin{bmatrix} 0 & 0 \\ 0 & 0 \end{bmatrix}$
(d) $\begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$
Step-by-Step Solution
A^2 = [[0,1],[1,0]] [[0,1],[1,0]] = [[1,0],[0,1]] = I. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Selecting $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$: 1.0 Mark
Correct Answer: $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$