First slide

Transpose of matrix

Question

If A and B are symmetric matrices, then AB – BA is a

Moderate

A

symmetric matrix
B

skew-symmetric matrix
C

diagonal matrix
D

null matrix

Solution

We are given $A^{'} = A, B^{'} = B$
Now $(A B - B A)^{'} = (A B)^{'} - (B A)^{'} = B^{'} A^{'} - A^{'} B^{'}$
$= B A - A B = - (A B - B A)$
i.e. $(A B - B A)^{'} = - (A B - B A)$
Hence, AB-BA is a skew-symmetric matrix.

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