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A square matrix A is called symmetric if
AA = -A^T
BA = A^T
CA^2 = A
DA^2 = I
Answer & Solution
Correct answer: B. A = A^T
1. Symmetric matrix satisfies a_{ij} = a_{ji} for every i, j.
2. This is equivalent to A equalling its transpose.
3. Hence A = A^T.
_Source: Maharashtra Balbharati Std XII Mathematics Part 1, Ch 2 "Matrices" §2.3_
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