Q65 of 307 Page 5

Give examples of matrices

A and B such that AB ≠ BA.

We need to find matrices A and B such that AB ≠ BA.


Let and.


First, we will find AB.






Now, we will find BA.






Thus, AB ≠ BA when and.


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If A is a square matrix, using mathematical induction prove that (AT)n = (An)T for all n ϵ N.

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A matrix X has a + b rows and a + 2 columns while the matrix Y has b + 1 rows and a + 3 columns. Both matrices XY and YX exist. Find a and b. Can you say XY and YX are of the same type? Are they equal?

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Give examples of matrices

A and B such that AB = O but A ≠ O, B ≠ O.

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Give examples of matrices

A and B such that AB = O but BA ≠ O.