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If A=[{:(1,0,-1),(2,1,3),(0,1, 1):}] the...

If `A=[{:(1,0,-1),(2,1,3),(0,1, 1):}]` then verify that `A^(2)+A=(A+I)` , where I is `3xx3` unit matrix.

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We have, `A=[{:(1,0,-1),(2,1,3),(0,1,1):}]`
`therefore A^(2)=A.A`
`=[{:(1,0,-1),(2,1,3),(0,1,1):}][{:(1,0,-1),(2,1,3),(0,1,1):}]=[{:(1,-1,-2),(4,4,4),(2,2,4):}]`
`therefore A^(2)+A=[{:(1,-1,-2),(4,4,4),(2,2,4):}]+[{:(1,0,-1),(2, 1,3),(0,1,1):}]`
`=[{:(2,-1,-3),(6,5,7) ,(2,3,5):}]`
Now, `A+I=[{:(1,0,-1),(2,1,3),(0,1,1):}]+[{:(1,0,0),(0,1,0),(0,0,1):}]=[{:(2,0,-1),(2,2,3),(0,1,3):}]`
and `A(A+I)=[{:(1,0,-1),(2,1,3),(0,1,1):}][{:(2,0,-1),( 2,2,3),(0,1,2):}]=[{:(2,-1,-3),(6,5,7),(2,3,5):}]`
Thus, we see that `A^(2)+A=A(A+I)`
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