# Equal matrices

Two matrices are said to be equal if they have the same order and each element of one is equal to the corresponding element of the other.

# Row matrix

A matrix having a single row is called a row matrix, e.g., [1 3 5 7].

# Column matrix

A matrix having a single column is called a column matrix, e.g., .

# Square matrix

An

*m*Ã—*n*matrix*A*is said to be a square matrix if*m*=*n,*i.e., number of rows = number of columns.The diagonal from the left-hand side upper corner to the right-hand side lower corner is known as leading diagonal or principal diagonal.

# Diagonal matrix

A square matrix all of whose elements, except those in the leading diagonal, are zero is called a diagonal matrix. For a square matrix

*A*= [*a*]_{ij}_{n}_{Ã—n }to be a diagonal matrix,*a*= 0, whenever_{ij}*i*â‰*j*.A diagonal matrix of order

*n*Ã—*n*having*d*_{1},*d*_{2}, ...,*d*as diagonal elements is denoted by diag [_{n}*d*_{1},*d*_{2}, ...,*d*]._{n}# Scalar matrix

A diagonal matrix whose all the leading diagonal elements are equal is called a scalar matrix.

For a square matrix

*A*= [*a*]_{ij}_{n}_{ Ã— n }to be a scalar matrix*a*= , where_{ij}*m*â‰ 0.# Unit matrix or identity matrix

A diagonal matrix of order

*n*, which has unity for all its diagonal elements, is called a unit matrix of order*n*and is denoted by*l*._{n}Thus, a square matrix

*A*= [*a*]_{ij}_{n}_{ Ã— n}is a unit matrix if*a*= ._{ij}# Triangular matrix

A square matrix in which all the elements below the diagonal are zero is called upper triangular matrix and a square matrix in which all the elements above diagonal are zero is called lower triangular matrix.

Given a square matrix

*A*= [*a*]_{ij}_{n }_{Ã— n}; for upper triangular matrix,*a*= 0,_{ij}*i*>*j*; and for lower triangular matrix,*a*= 0,_{ij}*i*<*j*.# Null matrix

If all the elements of a matrix (square or rectangular) are zero, it is called a null or zero matrix.

For

*A*= [*a*] to be null matrix,_{ij}*a*= 0 âˆ€_{ij}*i*,*j*.# Singular and non-singular matrix

A square matrix

*A*is said to be non-singular if |*A*| â‰ 0, and a square matrix*A*is said to be singular if |*A*| = 0.