Using elementary transformations, find the inverse of the matrix`[[1, 3,-2],[-3, 0,-5],[ 2, 5, 0]]`

Explanation

Let A = `[[1, 3,-2],[-3, 0,-5],[ 2, 5, 0]]`

We know that A=IA
`[[1, 3,-2],[-3, 0,-5],[ 2, 5, 0]]` = `[[1, 0,0],[0, 1,0],[ 0, 0, 1]]`A

`[[1, 3,-2],[-3, 9,-11],[ 0, -1, 4]]`=`[[1, 0,0],[3, 1,0],[ 2, 0, 1]]`A

(Using R2→R2+3R1 and R3→R3−2R1)

`[[1,3,-2],[0,1,-11/9],[0,-1,4]]``=``[[1,0,0],[1/3,1/9,0],[-2,0,1]]`A

Using
(R2→`1/9`R2)

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