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Using elementary transformations, find the inverse of the matrix`[3-1-4 2]`

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`Let A= [{:(3,-1),(-4,2):}]`
`Now , A=IA`
` implies[{:(3,-1),(-4,2):}]=[{:(1,0),(0,1):}]A`
`implies[{:(1,-(1)/(3)),(-4,2):}]=[{:((1)/(3),0),(0,1):}]A R_(1) to (1)/(3) R_(1)`
`implies [{:(1,-(1)/(3)),(0,(2)/(3)):}]=[{:((1)/(3),0),((4)/(3),1):}]A R_(2)to R_(2)+4R_(1)`
`[{:(1,-(1)/(3)),(0,1):}]=[{:((1)/(3),0),(2,(3)/(2):}]A R_(2) to (3)/(2)R_(2)`
`implies [{:(1,0),(0,1):}]=[{:(1,(1)/(2)),(2,(3)/(2)):}]A R_(1)_to R_(1) +(1)/(3) R_(2)`
`therefore A^(-1)=[{:(1,(1)/(2)),(2,(3)/(2):}]`
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