Q. 485.0( 1 Vote )

If A, B are squar

Answer :

A matrix is said to be skew-symmetric if A = -A’

Given, B is a skew-symmetric matrix.

∴ B = -B’

Let C = A’ BA …(1)

We have to prove C is skew-symmetric.

To prove: C = -C’

As C’ = (A’BA)’

We know that: (AB)’ = B’A’

⇒ C’ = (A’BA)’ = A’B’(A’)’

⇒ C’ = A’B’A {∵ (A’)’ = A}

⇒ C’ = A’(-B)A

⇒ C’ = -A’BA …(2)

From equation 1 and 2:

We have,

C’ = -C

Thus we say that C = A’ BA is a skew-symmetric matrix.

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation