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MATRICES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMATRICES1 Mark
MCQ
Choose the correct answer from the given four options.
If A and B are matrices of same order, then (AB′ – BA′) is a:
  • ✓
    Skew symmetric matrix.
  • B
    Null matrix.
  • C
    Symmetric matrix.
  • D
    Unit matrix.
✓

Answer

Correct option: A.
Skew symmetric matrix.
We have matrices A and B of same order.

Let P = (AB' - BA')

Then, P' = (AB' - BA')'

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

= (B')'(A)' - (A')'B' = BA' - AB' = -(AB' - BA') = -P

Hence, (AB' - BA') is a Skew symmetric matrix.

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