In mathematics, a **matrix** (plural **matrices**) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. For example, the dimension of the matrix below is `2 × 3` (read "two by three"), because there are two rows and three columns:
An `m × n` matrix: the `m` rows are horizontal, and the `n` columns are vertical. Each element of a matrix is often denoted by a variable with two subscripts. For example, <i>a<sub>2,1</sub></i> represents the element at the second row and first column of the matrix
## Operations on matrices
### Addition
To add two matrices: add the numbers in the matching positions:
We can multiply a matrix by a constant (the value 2 in this case):
![Matrices multiplication be a constant](https://www.mathsisfun.com/algebra/images/matrix-multiply-constant.gif)
### Multiplying by Another Matrix
To multiply a matrix by another matrix we need to do the [dot product](https://www.mathsisfun.com/algebra/vectors-dot-product.html) of rows and columns.
To work out the answer for the **1st row** and **1st column**: