Question

Give your own examples of matrices satisfying the following conditions:
A and B such that AB ≠ BA

Answer 1

Let A = `[(1, 2),(4, 5)]` and B = `[(3, 1),(5, 2)]`

AB =  `[(1, 2),(4, 5)] [(3, 1),(5, 2)]`

=`[(3 + 10, 1 + 4),(12 + 25, 4 + 10)]`

AB = `[(13, 5),(37, 14)]`   ......(1)

BA = `[(3, 1),(5, 2)] [(1, 2),(4, 5)]` 

= `[(3 + 4, 6 + 5),(5 + 8, 10 + 10)]`

BA = `[(7, 11),(13, 20)]`  ......(2)

From equation (1) and (2)

AB ≠ BA