If A is a symmetric and B is a skew symmetric matrix, then which of the following is correct?

Question

If A is a symmetric and B is a skew symmetric matrix, then which of the following is correct?, A B A T is a symmetric matrix, A B T + B A T is a symmetric matrix, A + B A - B is a skew symmetric matrix, A + I B - I is a skew symmetric matrix

MARKS App · Accepted Answer

A T = A , B T = - B A B A T T = A T T B T A T = - A B A T (Skew symmetric) A B T + B A T T = A B T T + B A T T = B A T + A B T = B A - A B = B A T + A B T (Symmetric) A + B A - B T = A - B T A + B T = A T - B T A T + B T = A + B A - B (Symmetric) A + I B - I T = B - I T A + I T = B T - I T A T + I T = - B - I A + I (neither symmetric nor skew symmetric)

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