linear algebra - Proving that a right (or left) inverse of a square matrix is unique using only basic matrix operations

Proving that a right (or left) inverse of a square matrix is unique using only basic matrix operations

-- i.e. without any reference to higher-order matters like rank, vector spaces or whatever ( :)).

More precisely, armed with the knowledge only of:

• rules of matrix equality check, addition, multiplication, distributive law and friends


• Gauss-Jordan elimination and appropriate equation system solution cases for the reduced row-echelon form

Thanks in advance.