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JAMIA 2021 — Mathematics PYQ

JAMIA | Mathematics | 2021

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

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Explanation

Properties of Matrices

Given that $A$ and $B$ are matrices of the same order. Let $C = AB' - BA'$ .

To determine the nature of matrix $C$ , we find its transpose $C'$ :

C' = (AB' - BA')'

Using the property $(X - Y)' = X' - Y'$ :

C' = (AB')' - (BA')'

Using the property $(XY)' = Y'X'$ and $(X')' = X$ :

C' = (B')'A' - (A')'B'

C' = BA' - AB'

Comparison

Now, factor out a negative sign:

C' = -(AB' - BA')

C' = -C

Conclusion

A square matrix $C$ is called skew-symmetric if $C' = -C$ .

Final Answer:

The matrix $(AB' - BA')$ is a Skew-Symmetric Matrix.

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