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Suppose a matrix A satisfies A^2-5A+7I=0...

Suppose a matrix A satisfies `A^2-5A+7I=0`. If `A^5=aA+bI`, then the value of `2a+b` is:

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`A^2 - 5A + 7I = 0`
`A^2 = 5A-7I`
`=>A^2*A = A(5A-7I)`
`=>A^3 = 5A^2-7A*I`
`=>A^3 = 5(5A-7I) - 7A`
`=>A^3 = 25A - 35I-7A`
`=>A^3 = 18A-35I`
`=>A^3*A = A(18A-35I)`
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