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Let A be a matrix of order 2xx2 such tha...

Let A be a matrix of order `2xx2` such that `A^(2)=O`.
`(I+A)^(100) =`

A

100 A

B

`100 (I+A)`

C

`100 I+A`

D

`I+100 A`

Text Solution

Verified by Experts

The correct Answer is:
D
`(I+A)^(100)= .^(100)C_(0)I^(100)+.^(100)C_(1)I^(99)A+.^(100)C_(2)I^(98) A^(2)+ +.^(100)C_(100)A^(100)`
`=I+100 A+O+O+ +O`
`=I+100 A`
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CENGAGE PUBLICATION-MATRICES-All Questions
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