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Let A= [[5,5alpha,alpha],[0,alpha,5alph...

Let ` A= [[5,5alpha,alpha],[0,alpha,5alpha],[0,0,5]]` .` If |A^2| = 25,` then `alpha` equals to:

A

`1/5`

B

5

C

`5^2`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`absA=5xxalphaxx5=25alpha[:'" A is an upper triangular matrix"]`
Now, `abs(A^2)=25`
`rArr abs(A^2)=25 rArr (25alpha)^2=25rArr alpha^2=-1/25rArrabsalpha=1/5`
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