The given matrix equation is :-

Let A =
and B = 
So, we can write the equation as
AP = B
Pre-multiplying A-1 both sides we get,
A-1AP = A-1B
IP = A-1B (
A-1A = I )
P = A-1B ( IP = P ) …….(i)
Now,
|A| =
= 1
and
adj A = 
A-1 =
adj A
A-1 = 
From (i) ,
= 
= 
Comparing both sides we get,
