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Using elementary transformations, find the inverse of the matrix`[[2,-3, 3],[ 2, 2, 3],[ 3,-2, 2]]`

Text Solution

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Let `A = [[2,-3,3],[2,2,3],[3,-2,2]]`
We know,
`A = AI`
`:. [[2,-3,3],[2,2,3],[3,-2,2]] = A[[1,0,0],[0,1,0],[0,0,1]]`
Applying `C_2->C_2+C_3` on both sides,
`[[2,0,3],[2,5,3],[3,0,2]] = A[[1,0,0],[0,1,0],[0,1,1]]`
Applying `C_1->C_3-C_1` on both sides,
`[[1,0,3],[1,5,3],[-1,0,2]] = A[[-1,0,0],[0,1,0],[1,1,1]]`
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