Matrices — Class 12 Maths Solution

ncert exercise SA NCERT,Ex.3.3,Q.No.11,Page.90
Question

If A, B are symmetric matrices of same order, then AB$-$BA is a

  • (a) Skew symmetric matrix
  • (b) Symmetric matrix
  • (c) Zero matrix
  • (d) Identity matrix
Step-by-step Solution

.:

Option a is correct

We know that, $A = A, B’ = B$

So, (AB - $BA)’ = (AB)’ - (BA)’$

= B’A’$-$A’B’ = BA$-$AB=$-$(AB$-$BA)

$\therefore$ AB$-$BA is a skew$-$symmetric matrix.

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Matrices. Curated by Sachin Sharma. Free for all students.