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If A=[[alpha,0],[ 1, 1]] and B=[[1, 0],[...

If `A=[[alpha,0],[ 1, 1]] and B=[[1, 0],[ 5, 1]],` find the values of `alpha` for which `A^2=Bdot`

A

1

B

-1

C

4

D

no real values

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`A^2=B`
`rArr {:[(alpha,0),(1,1)][(alpha,0),(1,1)]=[(1,0),(5,1)]:}`
`rArr {:[(a^2,0),(1,1)]=[(1,0),(5,1)]:}`
`rArr alpha^2-1 and alpha+1-5`
Clearly, these two equations are inconsistent.
Hence, there is no value of `alpha` satisfying `A^2=B`.
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