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