Now
AX = B
or
A–1 (AX) = A–1 B
(premultiplying by A–1)
or
(A–1A) X = A–1 B
(by associative property)
or
I X = A–1 B
or
X = A–1 B
This matrix equation provides unique solution for the given system of equations as
inverse of a matrix is unique This method of solving system of equations is known as
Matrix Method Case II If A is a singular matrix, then |A| = 0 In this case, we calculate (adj A) B