सर्वप्रथम हम इसको समीकरण के रूप में लिखते है।
A=IA
`{:[(1,2),(2,-1)]=[(1,0),(0,1)]:}`
`{:[(1,2),(0,5)]=[(1,0),(2,-1)]:}A," "R_(2)to2R_(1)-R_(2)`
`{:[(1,2),(0,1)]=[(1,0),((2)/(5),-(1)/(5))]:}A," "R_(2)to(1)/(5)R_(2)`
`{:[(1,0),(0,1)]=[((1)/(5),(2)/(5)),((2)/(5),-(1)/(5))]:}A," "R_(1)toR_(1)-2R_(2)`
अतः `{:A^(-1)=[((1)/(5),(2)/(5)),((2)/(5),-(1)/(5))]:}`