Question

Find the inverse of the matrix A=`[[1,2],[1,3]]` using elementry transformations.  

Answer 1

A=`[[1,2],[1,3]]` 

|A|=3-2

   =1≠ 0 

∴`A_1` exists

We have `A=A^-1=I` 

`[[1,2],[1,3]]A^1`=`[[1,0],[0,1]]` 

Applying` R_2→R_2-R_1` 

`[[1 ,2],[0,1]]A^1=[[1,0],[-1, 1]]` 

Applying `R_1→R_1-2R_2` 

`[[1,0],[0,1]]A^1=[[3,-2],[-1 ,1]]` 

Hence `A^-1=[[3,-2],[-1,1]]`