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If A=[(2,-3,-5),(-1 ,4 ,5),( 1,-3,-4)] ,...

If `A=[(2,-3,-5),(-1 ,4 ,5),( 1,-3,-4)]` , show that `A^2=A` .

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Given that,
`A=[(2,-3,-5),(-1 ,4 ,5),( 1,-3,-4)]`
`A^2=A*A`
`=[(2,-3,-5),(-1 ,4 ,5),( 1,-3,-4)][(2,-3,-5),(-1 ,4 ,5),( 1,-3,-4)]`
`=[(4+3-5,-6-12+15,-10-15+20),(-2-4+5,3+16-15,5+20-20),(2+3-4,-3-12+12,-5-15+16)]`
`=[(2,-3,-5),(-1 ,4 ,5),( 1,-3,-4)]`
`=A`
Hence `A^2=A`
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