Let A and B be any two 3 × 3 symmetric and skew symmetric matrices respectively. Then which of the following is NOT true?

Step-by-step solution

Given that A T = A , B T = - B Now solving all option one by one we get, Solving A option C = A 4 - B 4 C T = A 4 - B 4 = A 4 T - B 4 T = A 4 - B 4 = C ⇒ C = C T is a symmetric matrix Solving B option C = A B - B A C T = A B - B A T = A B T - B A T = B T A T - A T B T = - B A + A B = C ⇒ C = C T is a symmetric matrix Solving C option C = B 5 - A 5 C T = B 5 - A 5 T = B 5 T - A 5 T = - B 5 - A 5 ⇒ C ≠ C T   or   C ≠ - C T Solving D option C = A B + B A C T = A B + B A T = A B