A matrix represents a collection of numbers arranged in an order of rows and columns. It is necessary to enclose the elements of a matrix in parentheses or brackets. A matrix with 9 elements is shown below.

This Matrix [M] has 3 rows and 3 columns. Each element of matrix [M] can be referred to by its row and column number. For example, a_{23}=6

Order of a Matrix:

The order of a matrix is defined in terms of its number of rows and columns. Order of a matrix = No. of rows ×No. of columns Therefore Matrix [M] is a matrix of order 3 × 3.

Transpose of a Matrix :

The transpose [M]^{T} of an m x n matrix [M] is the n x m matrix obtained by interchanging the rows and columns of [M]. if A= [a_{ij}] mxn , then A^{T} = [b_{ij}] nxm where b_{ij} = a_{ji}

Properties of transpose of a matrix:

(A^{T})^{T}= A

(A+B)^{T}= A^{T} + B^{T}

(AB)^{T}= B^{T}A^{T}

Singular and Non-singular Matrix:

Singular Matrix: A square matrix is said to be singular matrix if its determinant is zero i.e. |A|=0

Nonsingular Matrix: A square matrix is said to be non-singular matrix if its determinant is non-zero.

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