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Question
Give your own examples of matrices satisfying the following conditions:
A and B such that AB = 0 = BA, A ≠ 0 and B ≠ 0
Solution
Let A = `[(x, - x),(-x, x)] ≠ 0`
B = `[(1, 1),(1, 1)] ≠ 0`
AB = `[(x, - x),(-x, x)] [(1, 1),(1, 1)]`
= `[(x - x, x - x),(-x + x, - x + x)]`
AB = `[(0, 0),(0, 0)]`
BA = `[(1, 1),(1, 1)] [(x, -x),(-x, x)]`
BA = `[(x - x, -x + x),(x - x, - x + x)]`
BA = `[(0, 0),(0, 0)]`
Martices A and B satisfies the condition
AB = 0 = BA
A ≠ 0
B ≠ 0.
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