NTA Abhyas JEE Main2020MathematicsMatricesPractice

If A 2 = A , then I + A 4 is equal to

Options

AI + 15 A
B1 + 7 A
C1 + 8 A
D1 + 11 A

Correct answer

A. I + 15 A

Step-by-step solution

As I and A commute, we can apply binomial theorem to expand 1 + A 4 , we have, I + A 4 = I + 4 A + 6 A 2 + 4 A 3 + A 4 But, A 3 = A 2 = A , A 4 = A 3 = A ( ∵ A 2 = A ) ∴ I + A 4 = I + 4 A + 6 A + 4 A + A = I + 15 A

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