Find the inverse of the matrix `A=[{:(1,3,3),(1,4,3),(1,3,4):}]` by using column transformations.

Explanation

The given matrix is `A=[{:(1,3,3),(1,4,3),(1,3,4):}]`
We know that, A = AI
`[{:(1,3,3),(1,4,3),(1,3,4):}]=A[{:(1,0,0),(0,1,0),(0,0,1):}]`
Applying `C_(2)toC_(2)-3C_(1),C_(3)toC_(3)-3C_(1),` we ,get
`[{:(1,0,0),(1,1,0),(1,0,1):}]=A[{:(1,-3,-3),(0,1,0),(0,0,1):}]`
Applying `C_(1)toC_(1)-C_(2)`, we get
`[{:(1,0,0),(0,1,0),(1,0,1):}]=A[{:(4,-3,-3),(-1,1,0),(0,0,1):}]`
Applying `C_(1)toC_(1)-C_(3)`, we get
`[{:(1,0,0),(0,1,0),(0,0,1):}]=A[{:(7,-3,-3),(-1,1,0),(-1,0,1):}]`
`A^(-1)=[{:(7,-3,-3),(-1,1,0),(-1,0,1):}]`