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Find Is Involutary matrix [[-5,-8,0],[3,5,0],[1,2,-1]]

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Your problem `->` Is Involutary matrix [[-5,-8,0],[3,5,0],[1,2,-1]]


A square matrix `A` is called an involutary matrix, if `A^2 = I` where `I` is the identity matrix.


`A` = 
`-5``-8``0`
`3``5``0`
`1``2``-1`


`A×A`=
`-5``-8``0`
`3``5``0`
`1``2``-1`
×
`-5``-8``0`
`3``5``0`
`1``2``-1`


=
`-5×-5-8×3+0×1``-5×-8-8×5+0×2``-5×0-8×0+0×-1`
`3×-5+5×3+0×1``3×-8+5×5+0×2``3×0+5×0+0×-1`
`1×-5+2×3-1×1``1×-8+2×5-1×2``1×0+2×0-1×-1`


=
`25-24+0``40-40+0``0+0+0`
`-15+15+0``-24+25+0``0+0+0`
`-5+6-1``-8+10-2``0+0+1`


=
`1``0``0`
`0``1``0`
`0``0``1`



Here `A^2 = I`, so `A` is an involutary matrix






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