If [[alpha, beta], [gamma, -alpha]] is t...

If `[[alpha, beta], [gamma, -alpha]]` is to be square root of two-rowed unit matrix, then `alpha,beta` and `gamma` should satisfy the relation. a. `1-alpha^2+betagamma=0` b. `alpha^2+betagamma=0` c. `1+alpha^2+betagamma=0` d. `1-alpha^2-betagamma=0`

A

`1-alpha^(2)+beta gamma=0`

B

`alpha^(2)+beta gamma-1=0`

C

`1+alpha^(2)+beta gamma=0`

D

`1-alpha^(2)-beta gamma=0`

Text Solution

Verified by Experts

The correct Answer is:

B

We have
`[(alpha,beta),(gamma,-alpha)][(alpha,beta),(gamma,-alpha)]=[(1,0),(0,1)]`
or `[(alpha^(2)+beta gamma,0),(0,alpha^(2)+beta gamma)]=[(1,0),(0,1)]`
or `alpha^(2)+beta gamma-1=0`

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