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Questions  

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

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a
skew symmetric  
b
symmetric   
c
neither symmetric not skew symmetric  
d
  I or -I, where I is an identity matrix

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detailed solution

Correct option is B

We are given A=A,B=B

Now        (ABBA)=(AB)(BA)=BAAB

=BAAB=(ABBA)

i.e.  (ABBA)=(ABBA)

Hence, AB-BA is a skew-symmetric matrix.

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