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Question
If A = `[(2, 4),(1, 3)]` and B = `[(1, 1),(0, 1)]` then find (A−1 B−1)
Solution
(A−1 B−1) = (BA)−1 .....[∵ (AB)−1 = B−1A−1]
∴ A = `[(2, 4),(1, 3)]`
A = (2 × 3) - (4 × 1)
A = 6 - 4
A = 2
∴ B = `[(1, 1),(0, 1)]`
B = (1 × 1) - (1 × 0)
B = 1 - 0
B = 1
(A−1 B−1) = `1/|"A"| ("adj A") * 1/|"B"| ("adj B")`
`= 1/2 [(3, -4),(-1, 2)] xx 1/1 [(1, -1), (0, 1)]`
`= 1/2 [(3, -4),(-1, 2)] [(1, -1), (0, 1)]`
`= 1/2 [(3, -7),(-1, 3)]`
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