If A and B are two square symmetric matrices of same order, then AB-BA is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → a skew-symmetric matrix
Let \(P = AB - BA\). Since A and B are symmetric, \(A' = A\) and \(B' = B\). By the reversal law for transposes, \((AB)' = B'A'\):
\(P' = (AB)' - (BA)'\)
\(= B'A' - A'B'\)
\(= BA - AB\)
\(= -P\)
Since \(P' = -P\), the matrix \(AB - BA\) is skew-symmetric.
NCERT (2026-27 edition):
Symmetric and Skew Symmetric Matrices
