Which of the following matrices have eigen values as 1 and -1 ?

Options

A. `[(0,1),(1,0)]`
B. `[(0, -i),(i,0)]`
C. `[(1,0),(0,-1)]`
D. `[(1,0),(0,1)]`

Explanation

(1) Characteristic determinant`=|(-lambda,1),(1,-lambda)|`
Thus, charactristic equation is
`lambda^(2)-1=0`
`:. lambda=1, -1`
(2) Characteristic determinant `=|(-lambda,-i),(i,-lambda)|`
Thus, characteristic equations is
`lambda^(2)-(-i^(2))=0` or `lambda^(2)-1=0`
`:. lambda=1, -1`
(3) Characteristic determinant `=|(1-lambda,0),(0,-1-lambda)|`
Thus, characteristic equation is
`lambda^(2)-1=0`
`:. lambda=1, -1`
(4) Characteristic determinant `=|(1-lambda,0),(0,1-lambda)|`
Thus, characteristic equation is
`(lambda-1)^(2)=0`
`:. lambda =1`