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Let A be a 3xx3 matric such that A . [(...

Let A be a `3xx3` matric such that
A . `[(1,2,3),(0,2,3),(0,1,1)]=[(0,0,1),(1,0,0),(0,1,0)]`, then find `A^(-1)`.

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We have, `A[(1,2,3),(0,2,3),(0,1,1)]=[(0,0,1),(1,0,0),(0,1,0)]`
To get `A^(-1)`, we have to transform this equation to `AB=I`. So, we will be using elementary column tranformations.
Applying `C_(1) harr C_(3)`, we get
`A[(3,1,2),(3,0,2),(1,0,1)]=[(1,0,0),(0,1,0),(0,0,1)]`
Applying `C_(2) harr C_(3)`, we get
`A[(3,1,2),(3,0,2),(1,0,1)]=[(1,0,0),(0,1,0),(0,0,1)]`
`implies A^(-1) =[(3,1,2),(3,0,2),(1,0,1)]`
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