How to get the inverse of a matrix 2 1 1 1 0 0 3 2 1 0 1 0 2 1 2 0 0 1 Make R1C1 to 1 by dividing by 1/2 1 0.5 0.5 0.5 0 0 3 2 1 0 1 0 2 1 2 0 0 1 Multiply Row 1 by 3 and subtract from row 3 R2 3 2 1 0 1 0 sub 3xR1 3 1.5 1.5 1.5 0 0 new R2 0 0.5 -0.5 -1.5 1 0 1 0.5 0.5 0.5 0 0 0 0.5 -0.5 -1.5 1 0 2 1 2 0 0 1 R3 2 1 2 0 0 1 sub 2 xR1 2 1 1 1 0 0 New R3 0 0 1 -1 0 1 1 0.5 0.5 0.5 0 0 0 0.5 -0.5 -1.5 1 0 0 0 1 -1 0 1 Make R2C2 pivot point 1 by multiply by 2 2 R2 0 1 -1 -3 2 0 1 0.5 0.5 0.5 0 0 0 1 -1 -3 2 0 0 0 1 -1 0 1 Multiply Row 2 by 0.5 .5 R 2 1 0.5 0.5 0.5 0 0 0 0.5 -0.5 -1.5 1 0 0 0 1 -1 0 1 Subtract R2 from R1 replace R1 R1 1 0.5 0.5 0.5 0 0 sub r2 0 0.5 -0.5 -1.5 1 0 new R1 1 0 1 2 -1 0 1 0 1 2 -1 0 0 1 -1 -3 2 0 0 0 1 -1 0 1 R1 1 0 1 2 -1 0 sub R3 0 0 1 -1 0 1 new R1 1 0 0 3 -1 -1 1 0 0 3 -1 -1 0 1 -1 -3 2 0 0 0 1 -1 0 1 Multiply R3 x -1 sub from R2 R2 0 1 -1 -3 2 0 sub -1 R3 0 0 -1 1 0 -1 new R2 0 1 0 -4 2 1 1 0 0 3 -1 -1 0 1 0 -4 2 1 0 0 1 -1 0 1 Check 2 1 1 3 -1 -1 1 0 0 3 2 1 -4 2 1 0 1 0 2 1 2 -1 0 1 0 0 1 A Inv A