Same chapter3 marksDifficulty: Medium
Prove that (AB)T = BTAT for matrices for which the product is defined.
Matrices
3 marksDifficulty: Medium
Define a symmetric and a skew-symmetric matrix, and state what can be said about the diagonal of a skew-symmetric matrix.
Original Khojo Papers practice question — not from a past board paper.
Answer
A square matrix A is symmetric if AT = A and skew-symmetric if AT = −A. Every diagonal element of a skew-symmetric matrix is zero, since a_ii = −a_ii forces a_ii = 0.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
Every square matrix can be written as the sum of a symmetric and a skew-symmetric matrix.
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