If A is a skew symmetric matrix of order 3 , B is a 3 × 1 column matrix and C = B T A B , then which of the following is false?

Question

If A is a skew symmetric matrix of order 3 , B is a 3 × 1 column matrix and C = B T A B , then which of the following is false?, C is singular, C is non singular, C is a symmetric matrix, C is a skew symmetric matrix

MARKS App · Accepted Answer

Given, C = B T A B C T = B T A B T ⇒ C T = B T A T B T T ⇒ C T = - B T A B = - C ⇒ C is skew symmetric ∵ order of C is 1 × 1 ⇒ C = 0 ⇒ C is singular and symmetric also.

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