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Matrices

NCERT Exemplar Class 12

CBSE

Grade 12

Question:

If $A$ and $B$ 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

(AB-BA)' = (AB)' - (BA)' = B'A' - A'B' = BA - AB = -(AB-BA). [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Selecting Skew-symmetric matrix: 1.0 Mark

Correct Answer: Skew-symmetric matrix

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