Ex 3.3, 11 - Chapter 3 Class 12 Matrices
Last updated at Jan. 17, 2020 by Teachoo
Last updated at Jan. 17, 2020 by Teachoo
Transcript
Ex 3.3, 11 If A, B are symmetric matrices of same order, then AB − BA is a A. Skew symmetric matrix B. Symmetric matrix C. Zero matrix D. Identity matrix A and B are symmetric matrices, ∴ A’ = A and B’ = B Consider (AB – BA)’ = (AB)’ – (BA)’ = B’A’ – A’B’ = BA − AB = − (AB – BA) ∴ (AB – BA)’ = − (AB – BA) Thus, (AB − BA) is a skew-symmetric matrix. ∴ Correct answer is A. [(A – B)’ = A’ – B’] [(AB)’ = B’A’] [By (1)]
Proof using property of transpose
Proof using property of transpose
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