In this paper I present selected properties of triangular matrices and basic properties of the rank of matrices over a field.
I define a submatrix as a matrix formed by selecting certain rows and columns from a bigger matrix. That is in my considerations, as an array, it is cut down to those entries constrained by row and column. Then I introduce the concept of the rank of a
At the end, I prove that the rank defined by the size of the biggest submatrix with a non-zero determinant of a matrix