If `[alphabetagamma-alpha]` is to be square root of two-rowed unit matrix, then `alpha,betaa n dgamma` should satisfy the relation. `1-alpha^2+betagam

Question

If `[alphabetagamma-alpha]` is to be square root of two-rowed unit matrix, then `alpha,betaa n dgamma` should satisfy the relation. `1-alpha^2+betagam

If `[alphabetagamma-alpha]` is to be square root of two-rowed unit matrix, then `alpha,betaa n dgamma` should satisfy the relation. `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`

Monjur Alahi

10 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

10 views Answered 2023-02-05 15:29