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Question: Answered & Verified by Expert
If A2=A, then I+A4 is equal to
MathematicsMatricesJEE Main
Options:
  • A I+15A
  • B 1+7A
  • C 1+8A
  • D 1+11A
Solution:
2629 Upvotes Verified Answer
The correct answer is: I+15A
As I and A commute, we can apply binomial theorem to expand 1+A4, we have,

I+A4=I+4A+6A2+4A3+A4

But, A3=A2=A, A4=A3=A   ( A 2 =A)

      I+A4=I+4A+6A+4A+A=I+15A  

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