A square n n matrix A is said to be non singular or invertible if there is another n n matrix B such that;
In this case the matrix B is called the inverse of A and is commonly denoted by A-1 rather than B. Otherwise the matrix A is called singular or non invertible.
Since AB = BA = I2, we conculde that B is the inverse of A.
Because of these uniqueness, we write the inverse of a non singular matrix A as A-1
Equating corresponding entries of these two matrices;
Since the matrix is;
We conclude that A is non singular matrices;