… matrix
square-matrix.
Algebraic structures of matrix’s
Indifferent unit
Definition:
… matrixsquare-matrix.
, 
Definition:
…unit-matrix
…is a square-matrix
The usual 
matrix has no indifferent unit, that is why we deal only with the square matrix’s.
For example:
, 
Inverse unit
Non square matrix’s has no inverse unit.
We are searching for: 
The inverse matrix is valid if the simultaneous linear equations are solvable. The equations are not solvable if the lines depend on each other in the linear way. They are, if the columns of the A matrix depends on each other in the linear way.
column-vectors: 
, 
row-vectors: 
, 
we can find a multiplicative inverse matrix for a matrix if its column-vectors do not depends on each other in the linear way.
Definition:
if the column-vectors are linear independent, than A is a regular matrix.
Definition:
if A is not a regular, than it is a singular one.
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