If A and B are matrices of same order, then (AB′ – BA′) is a

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Agniveer Navy SSR: 25th May 2025 Shift 2 Memory-Based Paper

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Answer 1

Concept:

Symmetric Matrix: Any square matrix A is said to be symmetric matrix if A' = A. where A' is the transpose of A.
Skew symmetric matrix: Any square matrix A is said to be symmetric matrix if A' = - A. where A' is the transpose of A.

Calculation:

Let P = (AB'- BA’)

∴ P' = (AB' - BA’)'

= (AB’)' — (BA’)'

= (B')'A' — (A')'B' [∵ (AB)' = BA]

= BA' - AB'

= - (AB'- BA’)

= - P

∴ P' = - P

So it is a skew symmetric matrix.