Row Matrix
A matrix having only one row is called a row-matrix.
For example: A[1 3 2 -2] is a row matrix of order 1 x 4.Column Matrix
A matrix having only one column is called a column matrix.
3 x 1 and 4 x 1 respectively.
Square Matrix
A matrix in which the number of rows is equal to the number of columns, say n, is called a square matrix of order n.In this square matrix of order n the elements a11, a22.......ann is called the principal diagonal or the leading diagonal.
The elements a11, a22,.......ann are called the diagonal elements of the square matrix.
Diagonal Matrix
A square matrix A=[aij]nxn is called a diagonal matrix if all the elements, except those in the leading diagonal, are zero.
i.e., aij = 0 for all i
jExample:
Scalar Matrix
A scalar matrix is a diagonal matrix in which all the diagonal elements are equal.
Example:
The matrices 
are scalar matrices of order 2 and 3 respectively.
Identity or Unit Matrix
A square matrix A=[aij]n x n is called an identity or unit matrix if
(2) aij =1 for all i = j
In other words a square matrix each of whose diagonal elements is unity and each of whose non-diagonal elements is equal to zero is called an identity or unit matrix. The identity matrix of order n is denoted by In.Example:
The matrices 
are identify matrices of order 2 and 3 respectively.
Null Matrix or Zero Matrix
A matrix of order m x n whose elements are all 0 is called a null matrix (or zero matrix) of order m x n. It is usually denoted by O or more clearly [O]m,n.
Example:
are all zero matrices of orders 1 x 2, 2 x 1, 2 x 2 and 3 x 3 respectively.
