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If A=[(4 ,3 ),(2 ,5)] , find x and y ...

If `A=[(4 ,3 ),(2 ,5)]` , find `x` and `y` such that `A^2-x A+y I=O` . Hence, evaluate `A^(-1)` .

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`A=[[4, 3],[2, 5]]` and `A^2-xA+yI=0`
`[(4 ,3 ),(2 ,5)] [(4 ,3 ),(2 ,5)]-x[(4 ,3 ),(2 ,5)]+y[[1, 0], [0,1]]=0`
`[[22-4x+y, 27-3x+0], [18-2x+0, 31-5x+y]]=[[0,0],[0,0]]`
`22−4x+y=0`
`=>4x−y=22------(1)`
`=>18−2x=0`
...
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