If `A=[(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)]` , then verify that `A^2+A=A(A+I)` , where `I` is the identity matrix.

Explanation

Given that,

`A=[(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)]`

`implies A^2= [(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)]xx [(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)]`

`implies A^2= [(1,-3,-6),(4,4,0),(2,2,4)] `

L.H.S.`=A^2+A= [(1,-3,-6),(4,4,0),(2,2,4)]+ [(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)]`

`=[(2,-3,-9),(6,5,3),(2,3,5)]`

R.H.S.`=A(A+I)= [(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)]( [(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)]+[(1,0,0),(0,1,0),(0,0,1)])`

`= [(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)][(2,0,-3),(2,2,3),(0,1,2)]`

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