For two unimobular complex numbers z(1) ...

For two unimobular complex numbers `z_(1)` and `z_(2)`, find `[(bar(z)_(1),-z_(2)),(bar(z)_(2),z_(1))]^(-1) [(z_(1),z_(2)),(-bar(z)_(2),bar(z)_(1))]^(-1)`

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The correct Answer is:

`[(1//2,0),(0,1//2)]`

`[(bar(z)_(1),-z_(2)),(bar(z)_(2),z_(1))]^(-1) [(z_(1),z_(2)),(-bar(z)_(2),bar(z)_(1))]`
`=([(z_(1),z_(2)),(-bar(z)_(2),bar(z)_(1))][(bar(z)_(1), -z_(2)),(bar(z)_(2),z_(1))])^(-1)`
`=[(z_(1)bar(z)_(1)+z_(2)bar(z)_(2),0),(0,z_(2)bar(z)_(2)+z_(1)bar(z)_(1))]^(-1)`
`=[(|z_(1)|^(2)+|z_(2)|^(2),0),(0,|z_(1)|^(2)+|z_(2)|^(2))]^(-1)`
`=[(2,0),(0,2)]^(-1)=[(1//2,0),(0,1//2)]`

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