सर्वप्रथम हम इसको समीकरण के रूप में लिखते है
A=IA
`{:[(2,3),(1,4)]=[(1,0),(0,1)]:}`
`{:[(1,-1),(1,4)]=[(1,-1),(0,1)]:}A," "R_(1)toR_(1)-R_(2)` के प्रयोग से
`{:[(1,-1),(1,-5)]=[(1,-1),(1,-2)]:}A," "R_(2)toR_(1)-R_(2)` के प्रयोग से
`{:[(1,-1),(0,1)]=[(1,-1),(-(1)/(5),(2)/(5))]:}A," "R_(2)to-R_(1)/(5)R_(2)` के प्रयोग से `{:[(1,0),(0,1)]=[((4)/(5),-(3)/(5)),(-(1)/(5),(2)/(5))]:}A," "R_(1)toR_(1)+R_(2)` के प्रयोग से
अतः `A^(-1)={:[((4)/(5),-(3)/(5)),(-(1)/(5),(2)/(5))]:}`
