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show that the matrix A=[(-5,-8,0),(3,...

show that the matrix
`A=[(-5,-8,0),(3,5,0),(1,2,-1)]` is involutory.

Text Solution

Verified by Experts

`A^(2)=A.A=[(-5,-8,0),(3,5,0),(1,2,-1)]xx[(-5,-8,0),(3,5,0),(1,2,-1)]`
`=[(25-24+0,40-40+0,0+0+0),(-1+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)]=I`
Hence , the given matrix A is involutory.
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