If A and B are symmetric matrices of the same order, then AB − BA is a:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → skew symmetric matrix
Since A and B are symmetric, \(A^T = A\) and \(B^T = B\). Using the reversal law \((AB)^T = B^TA^T\):
\((AB - BA)^T = (AB)^T - (BA)^T\)
\(= B^TA^T - A^TB^T\)
\(= BA - AB\)
\(= -(AB - BA)\)
A matrix whose transpose is its negative is skew symmetric. AB − BA is the zero matrix only when AB = BA, which is not true for symmetric matrices in general.
NCERT (2026-27 edition):
Symmetric and Skew Symmetric Matrices
