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If A=[1 2 3 3-2 1 4 2 1] , then show tha...

If `A=[1 2 3 3-2 1 4 2 1]` , then show that `A^3-23 A-401=0` .

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we have `A^(2)=A.A. =[{:(,1,2,3),(,3,-2,1),(,4,2,1):}]` `[{:(,1,2,3),(,3,-2,1),(,4,2,1):}]`=`[{:(,19,4,8),(,1,12,8),(,14,6,15):}]`
So, `A^(3)=A A^(2)=[{:(,1,2,3),(,3,-2,1),(,4,2,1):}]` `[{:(,1,2,3),(,3,-2,1),(,4,2,1):}]`=`[{:(,19,4,8),(,1,12,8),(,14,6,15):}]`
Now, `A(3)-23A=40I=[{:(,1,2,3),(,3,-2,1),(,4,2,1):}]``[{:(,1,2,3),(,3,-2,1),(,4,2,1):}]` -23 `[{:(,1,2,3),(,3,-2,1),(,4,2,1):}]`-40`[{:(,1,0,0),(,0,-1,0),(,0,0,1):}]`
`[{:(,63,46,69),(,69,-6,23),(,92,46,23):}]` `[{:(,-23,-46,-69),(,-69,46,-23),(,-92,-46,-23):}]`+`[{:(,-40,0,0),(,0,-40,0),(,0,0,-40):}]`
`[{:(,63 -23-40,46-46+40,69-69+0),(,69-69+0,-6+46-40,23-23+0),(,90-92+0,46-46+0,63-23-40):}]`=`[{:(,0,0,0),(,0,0,0),(,0,0,0):}]=O`
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