# Operations of Matrices

In order to add two matrices A and B, they must have the same number of rows and columns. Each element of the first matrix aij is added with the corresponding element of the second matrix bij and the result is an element cij in the same position in the resulting matrix. And a numerical example: ### Matrices Subtraction

In order to subtract two matrices A and B, they must have the same number of rows and columns. Each element of the second matrix bij is subtracted from the corresponding element of the first matrix aij and the result is an element cij in the same position in the resulting matrix. And a numerical example: ### Matrices Multiplication

In order to multiply two matrices A and B, the number of columns of the first matrix A must be equal to the number of rows of the second B. The resulting matrix C will have the number of rows of the first matrix A and the number of columns of the second matrix B. Each element cij of the resulting matrix is calculated as the summation of the product of each element of row i of matrix A, by the corresponding element of the column j of matrix B. This is quite complex and can be clarified by the following example: The first row of the resulting matrix C:

1X1+2X3+3X5=22

1X2+2X4+3X6=28

The second row of the resulting matrix C:

4X1+5X3+6X5=49

4X2+5X4+6X6=64

### Matrices Scalar Multiplication

A matrix A can be multiplied by a number k, multiplying each element of the matrix by this number.  ### Matrices Division

In order to divide two matrices A and B, we have to calculate the inverse of the second matrix and then multiply them. ### Matrices Scalar Division

A matrix A can be divided by a number k, dividing each element of the matrix by this number. Actually we scalar multiply matrix A by the inverse of the number k.           