MathematicsLet A and B be any two 3 × 3 matrices. If Ais symmetric and B is skew symmetric, thenthe matrix AB–BA is

Let A and B be any two 3 × 3 matrices. If Ais symmetric and B is skew symmetric, thenthe matrix AB–BA is

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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