To find the inverse of any arbitrary matrix like
a b
A

c d 
Step-01:
Evaluate the determinant of the matrix by cross multiplying the entries in the following
way STRICTLY
Determinant of A= A  ad  cb
STEP-02:
See if
A  0 , then no further proceedings & we conclude that inverse cant be found
But if A  0 , then it can found & proceed for next
Step-03:
Find the adjoint of ‘A’ as
 d b 
Adj ( A)  

 c a 
Finally
Step-04:
Inverse of A = Inv( A)  A1 
1
1  d b 
Adj ( A)  
.
A
A  c a 