A matrix in which a number of rows are equal to the number of columns is called a [b]square matrix[/b]. That is, a matrix of order [math]n\times n[/math] is often referred to as a square matrix of order [math]n[/math].

In a square matrix [math]A=\left[a_{ij}\right]_{n\times n}[/math] of order [math]n[/math], the elements [math]a_{11,}a_{22},a_{33},...,a_{nn}[/math] are called the[b] principal diagonal [/b]or simply the [b]diagonal [/b]or [b]main diagonal [/b]or [b]leading diagonal elements.[/b]

A square matrix [math]A=\left[a_{ij}\right]_{n\times n}[/math] is called a [b]diagonal matrix [/b]if [math]a_{ij}=0[/math] whenever [math]i\ne j.[/math]

A square matrix in which all the diagonal entries are 1 and the rest are all zero is called a [b]unit matrix[/b]. Thus, a square matrix [math]A=\left[a_{ij}\right]_{n\times n}[/math] is said to be a unit matrix if [math]a_{ij}=1[/math] if [math]i=j[/math], and [math]a_{_{ij}}=0[/math] if [math]i\ne j[/math].

A square matrix is said to be an [b]upper triangular matrix [/b]if all the elements below the main diagonal are zero.

A square matrix is said to be a [b]lower triangular matrix [/b]if all the elements above the main diagonal are zero.

A square matrix which is either [b]upper triangular or lower triangular [/b]is called a [b]triangular matrix.[/b]