A matrix is said to be skew-symmetric if A = -A’
Given, B is a skew-symmetric matrix.
Let
We have to prove C is skew-symmetric.
To prove: C = -C’
As
We know that: (AB)’ = B’A’
From equation 1 and 2:
We get,
C’ = -C
Thus, we say that C = A’ BA is a skew-symmetric matrix.