The matrix in mathematics is a rectangular or square array of numbers or variables, arranged in the form of rows and columns. Individual items in a matrix are known as elements or entries.

The size of the matrix is determined by some its rows and columns. Matrix with ‘m’ rows and ‘n’ columns is read as ‘m*n’ matrix where m and n are its dimensions.

$A=\left[\begin{array}{cccc}1& 2& 3& 4\\ 5& 6& 7& 8\\ 9& 10& 11& 12\end{array}\right]$

For example ,the matrix A mentioned above  is a 3*4 matrix ,where 1,5,9,2,6 etc are its elements.

Matrices Problems

Two matrices can be added or subtracted element by element, provided both are of the same size.

Below image will help us in understanding the addition and subtraction operation on matrices,

But there is a rule for matrix multiplication, the number of columns in the first matrix should be equal to a number of rows in the second.

If A is a matrix of m*n and B is a matrix of n*p then their product matrix C=(A*B) will be m*p, whose elements are produced by the dot product of a corresponding row of A and a corresponding column of B.

The above image gives us a better understanding of multiplication of matrices.