If A=[(1, 0),( 0 ,1)] , B=[(1 ,0),( 0,-1...

If `A=[(1, 0),( 0 ,1)]` , `B=[(1 ,0),( 0,-1)]` and `C=[(0, 1),( 1 ,0)]` , then show that `A^2=B^2=C^2=I_2` .

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Verified by Experts

Given that,
`A=[(1, 0),( 0 ,1)]`
`B=[(1 ,0),( 0,-1)]`
`C=[(0, 1),( 1 ,0)]`
`A^2=[(1, 0),( 0 ,1)][(1, 0),( 0 ,1)]`
`=[(1,0),(0,1)]=I_2`
`B^2=[(1, 0),( 0 ,-1)][(1, 0),( 0 ,-1)]`
`=[(1,0),(0,1)]=I_2`
`C^2=[(0, 1),( 1 ,0)][(0, 1),( 1 ,0)]`
`=[(1,0),(0,1)]=I_2`
hence,`A^2=B^2=C^2=I_2`

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