GATE ME 2025 Set 1 — Question 11
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Engineering Mathematics → Linear Algebra → Matrix Algebra & Operations
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Question
Let A and B be real symmetric matrices of same size. Which one of the following options is correct?
Correct answer
(C) (AB)^T = B^T A^T
Solution
The property is a fundamental identity in matrix algebra that holds for any two matrices and for which the product is defined. It is independent of whether the matrices are symmetric or not. Options A, B, and D are not generally true for all real symmetric matrices.
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