Let A and B be any two \(3\times 3\) matrices. If A is symmetric and B is skewsymmetric, then the matrix AB \(-\) BA is :
Show Hint
- skewsymmetric
- symmetric
- neither symmetric nor skewsymmetric
- I or \(-\)I, where I is an identity matrix.
The Correct Option is B
Solution and Explanation
\((AB-BA)^T=(AB)^T-(BA)^T=B^TA^T-A^TB^T=(-B)A-A(-B)=-BA+AB\).
So \((AB-BA)^T=AB-BA\): the matrix is symmetric.
Answer: (2) symmetric
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