Matrices are tables of numbers. The numbers are put inside big brackets. Matrices are given 'orders', which basically describe the size of the matrices. The order is the number of rows 'by' the number of columns. So a 2 by 3 matrix has 2 rows and 3 columns.

Adding and Subtracting
Adding and subtracting matrices is fairly straight-forward. Adding and subtracting of matrices, however, can only occur if the matrices have the same order.

Multiplication
This is a little harder than addition and subtraction. Multiplication cannot occur between any two matrices just like addition can't occur between any two matrices- they have to be compatible.
The rule is: if you want to multiply two matrices, if the first matrix has order p×q (p by q) and the second has order y×z, q must equal y or you can't multiply the two matrices. If you can multiply, the answer will be a matrix which has order p×z.
Here is how you would multiply a 2×3 and a 3×2 matrix:

Example: