Matrix: A matrix is a rectangular arrangement of “mn” elements with ‘m’ rows and ‘n’ columns enclosed within brackets.
Here m x n is called the order of the matrix and it should be read as “m by n”.
Example: 
is a matrix with 2 rows and 2 columns. So, is a matrix of order 2×2.
Example:
is a matrix of order 2×3.
Principal diagonal: The elements for which the row number and column number is same are called the elements of the “principal diagonal”.
Example :1,4 are the elements in the principal diagonal of .
Types of matrices:
a) Column matrix: It is a matrix with only one column.
Example: 
b) Row matrix: It is a matrix with only one row.
Example: [1 2 -5] 1×3
c) Null matrix: It is a matrix of order mxn where all the elements as zero es is called a null matrix and is denoted by Omxn.
Example:
d) Rectangular matrix: It is a matrix where the number of rows is not equal to number of columns.
Example:
e) Square matrix: It is a matrix where the number of rows is equal to number of columns. A square matrix of order nxn is called as a square matrix of order ‘n’.
Example:
is a square matrix of order 2.
f) Diagonal matrix: It is a square matrix where diagonal elements are non zeroes and the rest are zeroes.
Example: 
.
g) Scalar matrix: It is a diagonal matrix where all the diagonal elements are equal.
Example: 
.
h) Unit or Identity matrix: It is a diagonal matrix where all the diagonal elements are equal to 1. An identity matrix of order mxm is denoted by Im.
Example: 
.
i) Lower triangular matrix: It is a square matrix where all the non diagonal elements above the principal diagonal are zeroes.
Example: 
.
j) Upper triangular matrix: It is a square matrix where all the non diagonal elements below the principal diagonal are zeroes.
Example:
.
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