Matrix A such that A2 =2A - I where I is the identity matrix, then for n≥2, An is equal to

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2n−1A−(n−1)I

2n−1A−I

nA−(n−1)I

nA−I

answer is C.

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Detailed Solution

Given A2 =2A - INow A3=AA2=A(2A−I)=2A2−A=2(2A−I)−A=3A−2IA4=AA3=A(3A−2I)=3A2−2A=3(2A−I)−2A=4A−3IFollowing this, we can say An=nA−(n−1)I

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