Let $A$ be a $2 \times 2$ matrix with all entries non-zero, and let $A^2 = I$, where $I$ is the identity matrix. Then the trace of $A$ is:
Step-by-Step Solution
Key Concept: Write $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$ with all of $a, b, c, d$ non-zero, impose $A^2 = I$ entry-wise, and deduce what the off-diagonal conditions force the diagonal entries $a, d$ to satisfy.
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Correct Answer: (3)