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

If `A=[[2,-2,-4],[-1,3,4],[1,-2,-3]]` then A is `1) an idempotent matrix 2) nilpotent matrix 3) involutary 4) orthogonal matrix

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`A^(2)=AxxA=[(2,-2,-4),(-1,3,4),(1,-2,-3)]xx[(2,-2,-4),(-1,3,4),(1,-2,-3)]`
`=[(4+2-4,-4-6+8,-8-8+12),(-2-3+4,2+9-8,4+12-12),(2+2-3,-2-6+6,-4-8+9)]`
`=[(2,-2,-4),(-1,3,4),(1,-2,-3)]`
`=A`
Hence, the matrix A is idempotent.
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