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Question
If A = `[(0, 1),(2, 3),(1, -1)]` and B = `[(1, 2, 1),(2, 1, 0)]`, then find (AB)−1
Solution
AB = `[(0, 1),(2,3),(1, -1)] [(1, 2, 1),(2, 1, 0)]`
= `[(0 + 2, 0 +1, 0 + 0),(2 + 6, 4 + 3, 2 + 0),(1 - 2, 2 - 1, 1 + 0)]`
= `[(2, 1, 0),(8, 7, 2),(-1, 1, 1)]`
∴ |AB| = `2|(7, 2),(1, 1)| -1|(8, 2),(-1, 1)| + 0`
= 2(7 – 2) – (8 + 2)
= 10 – 10
= 0
∴ (AB)−1 does not exist.
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