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

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

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Given that, `A=[(0,-x),(x,0)]` , `B=[(0 ,1 ),(1 ,0)]`
`therefore A^2=[(-x^2,0),(0,-x^2)]`
`B^2=[(1,0),(0,1)]`
And `A+B=[(0,-x),(x,0)]+[(0 ,1 ),(1 ,0)]`
`implies A+B=[(0,-x+1),(x+1,0)]`
Now, `(A+B)^2=[(1-x^2,0),(0,1-x^2)]`
It is given that, `x^2=-1`
...

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