There are several types of matrices, but most commonly used are:

Rows Matrix

Columns Matrix

Rectangular Matrix

Square Matrix

Diagonal Matrix

Scalar Matrix

Identity Matrix

Triangular Matrix

Null or Zero Matrix

Transpose of a Matrix
Row Matrix:
A matrix is said to be row matrix if it has only one row.
e.g.
Column Matrix:
A matrix is said to be column matrix if it has only one column.
e.g.
Rectangular Matrix:
A matrix is said to be rectangular if number of rows is not equal to number of columns.
e.g.
Square Matrix:
A matrix is said to be square if number of its rows is equal to number of its columns.
e.g.
Diagonal Matrix:
A square matrix is said to be diagonal if at least one elements of principal diagonal is nonzero and all other elements are zero.
e.g.
Scalar Matrix:
A diagonal matrix is said to be scalar if all of its diagonal elements are same.
e.g.
Identity or Unit Matrix:
A diagonal matrix is said to be identity if all of its diagonal elements equal to one, denoted by .
e.g.
Triangular Matrix:
A square matrix is said to be triangular if all of its elements below principal diagonal are zero (Lower Triangular Matrix) or all of its elements above principal diagonal are zero (Upper Triangular Matrix).
e.g:
! (Lower Triangular Matrix)
(Upper Triangular Matrix)
Null or Zero Matrix:
A matrix is said to be null or zero matrix if all of its elements, equal to zero. It is denoted by .
e.g.
Transpose of a Matrix:
Suppose be a given matrix, then the matrix obtained by interchanging its rows into columns is called Transpose of , it is denoted by .
e.g.
Let
then