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[{:(3,1),(5,2):}] using elementry method...

`[{:(3,1),(5,2):}]` using elementry method find the inverse of matrix

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`Let A=[{:(3,1),(5,2):}]`
` now ,A=IA `
`implies [{:(3,1),(5,2):}]=[{:(1,0),(0,1):}]A R_(1) to(1)/(3) R_(1) `
`implies [{:(1,(1)/(3)),(5,2):}]=[{:((1)/(3),),((-5)/(3),1):}]A R_(2) to R_(2)-5R_(1)`
`implies [{:(1,(1)/(3)),(0,1):}]=[{:((1)/(3) ,0),( -5,3):}]A R_(2) to 3R_(2)`
`implies [{:(1,0),(0,1):}]=[{:(2,-1),(-5,3):}]A R_(1)to R_(1)-(1)/(3)R_(1)`
`therefore A^(-1)=[{:(2,-1),(-5,3):}]`
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