If the square of the matrix `[(alpha,beta),(gamma,-alpha)]` is the unit matrix of order 2, then `alpha, beta` and `gamma` should satisfy the relation.

Options

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`

Answer

B

Explanation

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`