Question:
If A, B are square matrices of same order and B is a skew-symmetric matrix,
show that A¢BA is skew symmetric.
Solution:
Given, A and B are square matrices such that B is a skew-symmetric matrix
So, B¢ = -B
Now, we have to prove that A¢BA is a skew-symmetric matrix.
(A¢BA) ¢ = A¢B¢ (A¢)¢ [Since, (AB) ¢ = B¢A¢]
= A¢ (-B)A
= -A¢BA
Hence, A¢BA is a skew-symmetric matrix.