Column Matrix

A matrix is said to be a column matrix if it has only one column.  In general, a = [a_ij] _{m x 1} is a column matrix of order m x 1
                      
For example:    
                               
Order of A is 3 x 1 and that of B is 4 x 1

Row Matrix

A matrix is said to be a row matrix if it has only one row.  In general,           B = [b_ij] _{1 x n} is a row matrix of order 1 x n

For example: A = [2  0  5  -3]        B = [1/2  0   √3     6    7]
Here order of A is 1 x 4 and that of B is 1 x 5

Square Matrix

A matrix whose numbers of columns are equal to number of rows is said to be a square matrix.  Thus an m x n matrix is said to be a square matrix if m = n and is known as a square matrix of order ‘n’.
                                
For example:    
                                                                  
Hence A is of order 3 and B is of order 2.

Diagonal Matrix

A square matrix B = [bij]mxm is said to be a diagonal matrix if all its non diagonal elements are zero.
                                                         
For example:
                                     

Hence the orders of A, B and C are 1,2 and 3 respectively

Scalar Matrix

A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal.
That is b_ij = 0, when i ≠ j
           b_ij = k, when i = j, for some constant k
                                                                  
For example:
Hence the order of A, B and C are 1, 2 and 3 respectively.

Identity Matrix

A square matrix in which elements in the diagonal are all 1 and rest all are zero is called and identity matrix.  In other words, the square matrix A =

Zero Matrix

A matrix is said to be a zero matrix if all its entries are zero.  Another name for zero matrix is null matrix.  It is denoted by 0.
                                       
For example:   
The orders of the above matrices are 1 x 1, 2 x 2 and 2 x 3 respectively.

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Reference Links:

• http://simple.wikipedia.org/wiki/Matrix_(mathematics)#One_column_matrix
• http://en.wikipedia.org/wiki/Row_matrix
• http://www.britannica.com/EBchecked/topic/561660/square-matrix
• http://en.wikipedia.org/wiki/Diagonal_matrix
• http://en.wikipedia.org/wiki/Diagonal_matrix#Scalar_matrix
• http://en.wikipedia.org/wiki/Identity_matrix
• http://en.wikipedia.org/wiki/Zero_matrix