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Find Is Idempotent matrix [[2,-2,-4],[-1,3,4],[1,-2,-3]]

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Your problem `->` Is Idempotent matrix [[2,-2,-4],[-1,3,4],[1,-2,-3]]


A square matrix `A` is called an idempotent matrix, if `A^2 = A`.


`A` = 
`2``-2``-4`
`-1``3``4`
`1``-2``-3`


`A×A`=
`2``-2``-4`
`-1``3``4`
`1``-2``-3`
×
`2``-2``-4`
`-1``3``4`
`1``-2``-3`


=
`2×2-2×-1-4×1``2×-2-2×3-4×-2``2×-4-2×4-4×-3`
`-1×2+3×-1+4×1``-1×-2+3×3+4×-2``-1×-4+3×4+4×-3`
`1×2-2×-1-3×1``1×-2-2×3-3×-2``1×-4-2×4-3×-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`



Here `A^2 = A`, so `A` is an idempotent matrix






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