A matrix A is such that A2=2A−I, where I is unity matrix, then for n≥2, An is equal to
A
nA−(n−1)I
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B
nA−I
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C
2n−1A−(n−1)I
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D
2nA−nI
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Solution
The correct option is AnA−(n−1)I A2=2A−I Let us calculate A3 A3=A2A ⇒A3=(2A−I)A⇒A3=2A2−A⇒A3=2(2A−I)−A⇒A3=3A−2I Lets calculate A4 A4=3A2−2A⇒A4=3(2A−I)−2A⇒A4=4A−3I Similarly we can write, An=nA−(n−1)I