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.**