The word “matrices” can be defined as the rectangular positioning of numbers in the pattern of rows and columns. For example;  is matrix of order 2 × 3, where 2 represents the count of the rows, and 3 represents the count of the columns.

A general m × n matrix is of the form,

The row number is given by horizontal (m) and columns by vertical (n). The general representation of an element of a matrix is with 2 subscripts. For instance, a2,1 represents the element in the first column and the second row of the given matrix.

Basic Operations On Matrices

1] Matrix Addition

Two matrices can be added, as long as the orders of both matrices are the same. The process of addition is adding the corresponding elements in the same positions.

2] Matrix Subtraction

The method of matrix subtraction is alike matrix addition. Two matrices can be subtracted, as long as the orders of both matrices are the same. The process of finding the difference is by subtracting the corresponding elements in the same positions.

3] Matrix Multiplication

Two matrices of the same order can be multiplied, if the count of the columns of the first matrix is equal to the number of rows of the second matrix. It is generally written as A (B) or  (A) B.

4] Transpose Of A Matrix

The transpose of a matrix can be obtained by swapping the rows and columns of the matrix given.

5] Inverse Of A Matrix

The inverse of a matrix can be computed using the formula,

A-1 = adj (A) / determinant of A

Information relevant to the topic of matrices is explained above. For more information on various mathematical concepts such as permutations, combinations, calculus, determinants, differential equations, differentiation, integration etc., refer to BYJU’S website. It contains detailed explanations along with solved problems.