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If A =[[l(1),m(1),n(1)],[l(2),m(2),n(2)]...

If A =`[[l_(1),m_(1),n_(1)],[l_(2),m_(2),n_(2)],[l_(3),m_(3),n_(3)]]` then Find `A+I`

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`Let A =[[l_(1) , m_(1), n_(1)],[l_(2), m_(2), n_(2) ],[l_(3),m_(3),n_(3)]]`
`therefore A^(T) = [[l_(1),l_(2), 1_(3)],[m_(1) ,m_(2),m_(3) ],[n_(1),n_(2),n_(3)]]`
Now, `A A^(T) =[[l_(1) , m_(1), n_(1)],[l_(2), m_(2), n_(2) ],[l_(3),m_(3),n_(3)]]xx [[l_(1),l_(2), 1_(3)],[m_(1) ,m_(2),m_(3) ],[n_(1),n_(2),n_(3)]]`
`= [[Sigmal_(1)^(2),Sigmal_(1) l_(2) ,Sigmal_(3)l_(1)],[Sigmal_(1)l_(2),Sigmal_(2)^(2), Sigmal_(2)l_(3) ],[Sigmal_(3)l_(1), Sigmal_(2)l_(3),Sigmal_(3)^(2)]]= [[1,0,0],[0,1,0],[0,0,1]]=I`
Hence, matrix A is orthogonal.
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