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Suppose matrix $A$ satisfies the equation $A^{2} - 5 A + 7 I = O .$ If $A^{8} = a A + b I,$ then value of $a$ is

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Correct option is A

A2=5A−7I⇒A4=A22=(5A−7I)(5A−7I)=25A2−70A+49I=25(5A−7I)−70A+49I=55A−126I⇒ A8=A42=(55A−126I)(55A−126I)=3025A2−13860A+15876I=3025(5A−7I)−13860A+158766I=1265A−5299IThus, a=1265.

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Suppose matrix A satisfies the equation A2-5A+7I=O. If A8=aA+bI, then value of a is

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Ready to Test Your Skills?

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Suppose matrix $A$ satisfies the equation $A^{2} - 5 A + 7 I = O .$ If $A^{8} = a A + b I,$ then value of $a$ is