First slide

Transpose of matrix

Question

If A and B are two skew-symmetric matrices of order n, then

Moderate

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

Solution

We are given $A^{'} = - A$ and $B^{'} = - B$
Now, $(A B)^{'} = B^{'} A^{'} = (- B) (- A) = B A$
$= A B$ if A and B commute.

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