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Show that A=[[-8 ,5] ,[2, 4]] satisfies ...

Show that `A=[[-8 ,5] ,[2, 4]]` satisfies the equation `A^2+4A-42 I=O` . Hence, find `A^(-1)` .

Text Solution

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`A=[[-8, 5], [2, 4]]`
`A^2=[[-8, 5], [2, 4]] [[-8, 5], [2, 4]]`
`=[[74, -20], [8, 26]]`
`4A=[[32, 20], [8, 16]]`
`42I=[[42, 0], [0, 42]]`
`A^2+4A-42I=[[0, 0], [0, 0]]`
`A^2+4A-42I=0=>A^(-1)=1/42(A+4I)`
`1/42[[-4, 5], [2, 8]]`
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