# Determinant of a Matrix

A determinant of a matrix
is a **real** number associated with a square matrix. The determinant of a matrix
holds important information about the nature of a matrix. It is important to remember
that only square matrices have determinants, so as not to waste time attempting
to find the determinant of a non square matrix.

The determinant of a matrix **A** is denoted by

or with the parentheses as

All size n x n have determinants but we are only going to focus on determinants of matrices of size 2 x 2 and 3 x 3

Given a 2 x 2 matrix **A**

the determinant of **A** is given by

Given a matrix **B** of size 3 x 3

the determinant of **B** is given by

Try to memorize the formulae above or do a lot of practice problems so that they become easy to remember. Below are some examples:

## Examples of Matrix Determinants

**Example 1:** Find **det****M** given that

Solution:

**Example 2:** Find the determinant of the matrix **A** given below:

Solution:

## Quiz on Determinants