Definition 5 A square matrix A is said to be non-singular if A  ≠ 0
Let
A = 
1
2
3
4





 Then A = 
1
2
3
4  = 4 – 6 = – 2 ≠ 0 Hence A is a nonsingular matrix
We state the following theorems without proof Theorem 2 If A and B are nonsingular matrices of the same order, then AB and BA
are also nonsingular matrices of the same order