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If A=[1 2 2 2 1 2 2 2 1] , find A^(-1) a...

If `A=[1 2 2 2 1 2 2 2 1]` , find `A^(-1)` and prove that `A^2-4A-5I=O` .

Text Solution

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`A^2=A xx A`
`=[[9, 8, 8], [8, 9, 8], [8, 8, 9]]`
`4A=[[4, 8, 8], [8, 4, 8], [8, 8, 4]]`
`5I=[[5, 0, 0], [0, 5, 0], [0, 0, 5]]`
`A^2-4A-5I=[[0, 0, 0], [0, 0, 0], [0, 0, 0]] `
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