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CGP EDU Academic Team
Published on: August 14, 2026
Let A and B be any two 3x3 symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?
Text Solution
Verified by ExpertsThe correct answer is:
C
Given that A T = A, B T = -B
C = A 4 -B 4
C T = (A 4 -B 4 ) = (A 4 ) T -(B 4 ) T = A 4 -B 4 = C
C = AB - BA
C T = (AB - BA) T = (AB) T - (BA) T
= B T A T - A T B T = -B A + AB = C
C = B 5 - A 5
C T = (B 5 - A 5 ) T = (B 5 ) T - (A 5 ) T = -B 5 - A 5
C = AB + BA
C T = (AB + B A) T = (AB) T + (B A) T
= -BA-AB=-C
Option C is not true
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