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Show that A=[[6, 5], [7, 6]] satisfies t...

Show that `A=[[6, 5], [7, 6]]` satisfies the equation `x^2-12 x+1=0` . Thus, find `A^(-1)`

Text Solution

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`A=[[6, 5],[7, 6]]`
`A^2=[[6, 5],[7, 6]] [[6, 5],[7, 6]]=[[71, 60], [84, 71]]`
`A^2-12A+I=[[0,0], [0,0]]`
`A^2-12A+I=0`
`A` satisfies the equation `x ^2 −12x+1=0`
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