If `A=[[1,-1],[2,-1]],B=[[a,1],[b, -1]]` and `(A+B)^2=A^2+B^2`, find the values of `a` and `b`

Explanation

Given that,

`A=[[1,-1],[2,-1]],B=[[a,1],[b, -1]]`


`A+B=[[1,-1],[2,-1]]+[[a,1],[b, -1]]=[[a+1,0],[b+2, -2]]`


`Rightarrow (A+B)^2 = [[a+1,0],[b+2, -2]][[a+1,0],[b+2, -2]]`


`Rightarrow (A+B)^2 = [[a^2+1+2a ,0],[2+2a+b+ab-4-2b, 4]]`


`Rightarrow (A+B)^2 = [[a^2+1+2a ,0],[2a+ab-2-b, 4]]`


Now,

`A^2 + B^2 = [[1,-1],[2,-1]][[1,-1],[2,-1]]+[[a,1],[b, -1]][[a,1],[b, -1]]`


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