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Question
Given `A = [(2,-3),(-4,7)]` compute `A^(-1)` and show that `2A^(-1) = 9I - A`
Solution
`A = [(2,-3),(-4,7)]`
|A| = 14 - 12 = 2
`:. A_11 = 7` `A_12 = 4` `A_31 = 3` `A_22 = 2`
`adj(A) = [(A_11,A_22),(A_21,A_22)]^T = [(7,4),(3,2 )]^T = [(7,3),(4,2)]`
`:. A^(-1) = I/(|A|) adj (A) = 1/2 [(7,3),(4,2)]`
L.H.S = `2A^(-1) = [(7,3),(4,2)]`
R.H.S = `9I - A = [(9,0),(0,9)] - [(2,-3),(-4,7)] = [(7,3),(4,2)]`
L.H.S = R.H.S
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