Question
Question: If A and B are two skew symmetric matrices of order n, then-...
If A and B are two skew symmetric matrices of order n, then-
A
AB is a skew symmetric matrix
B
AB is a symmetric matrix
C
AB is a symmetric matrix if A and B commute
D
None of these
Answer
AB is a symmetric matrix if A and B commute
Explanation
Solution
We are given
A¢ = –A and B¢ = –B
Now, (AB)¢ = B¢A¢ = (–B) (–A) = BA
= AB if A and B commute.