For example:

b, multiply the i-th column or row by ()

For example:

2.row*2 now the matrix had also changed.

c, i-th row or column +-th row or column

d, change two rows or columns.

It is only possible if we use only the rows or only the columns. They must not be mixed with each other.

Theorem: the elements of any matrix can be transformed to a triangle-shape.

Proof: without proof.

Theorem: Any square-matrix can be transformed to a diagonal one.

Proof: without proof.

Theorem: every regular matrix can be transformed to a unit-matrix.

Proof: without proof.

By mixing the unit matrix with the same transformations as the basic matrix, we can get the inverse matrix.

Expl. A=

II-2*I

I-3*II

I/2

Definition:

A regular matrix

A… self-inverse matrix.