Question

Give your own examples of matrices satisfying the following conditions:
A and B such that AB = 0 and BA ≠ 0

Answer 1

Let A = `[(0, 1),(0, 0)]` and B = `[(1, 0),(0, 0)]`

AB = `[(0, 1),(0, 0)] [(1, 0),(0, 0)]`

= `[(0 + 0, 0 + 0),(0 + 0, 0 + 0)]`

= `[(0, 0),(0, 0)]`

AB = 0

BA = `[(1, 0),(0, 0)] [(0, 1),(0, 0)]`

= `[(0 + 0, 1 + 0),(0 + 0, 0 + 0)]`

= `[(0, 1),(0, 0)]`

BA ≠ 0

∴ AB = 0 and BA ≠ 0