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MATRICES — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMATRICES1 Mark
Question
Choose the correct answer from the given four options.
If A and B are matrices of same order, then (AB′ – BA′) is a:
  1. Skew symmetric matrix.
  2. Null matrix.
  3. Symmetric matrix.
  4. Unit matrix.
✓

Answer

  1. Skew symmetric matrix.
Solution:
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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