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Find the inverse of the matrix A=[{:(1...

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

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`|A|= |(1,3,3),(1,4,3),(1,3,4)|`
` = 1(16-9) - 3 (4 -3)+ 3(3-4)`
` = 7 - 3 - 3 = 1 ne 0`
` :. A^(-1)` exists.
Consider `A^(-1) A = I`
`:. A^(-1) {:((1,3,3),(1,4,3),(1,3,4)):}={:((1,0,0),(0,1,0),(0,0,1)):}`
By `C_(2) - 3C_(1) and C_(3) - 3C_(1)` we get,
` A^(-1) {:((1,0,0),(1,1,0),(1,0,1)):}={:((1,-3,-3),(0,1,0),(0,0,1)):}`
By `C_(1) - C_(2)` , we get,
` A^(-1) {:((1,0,0),(1,1,0),(1,0,1)):}={:((4,-3,-3),(-1,1,0),(0,0,1)):}`
By `C_(1) - C_(3)`, we get,
` A^(-1) {:((1,0,0),(0,1,0),(0,0,1)):}={:((7,-3,-3),(-1,1,0),(-1,0,1)):}`
`:. A^(-1) = {:((7,-3,-3),(-1,1,0),(-1,0,1)):}`.
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