If A, B are square matrices of same order

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.

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now