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# 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 detM given that

Solution:

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

Solution:

1.

-335

2.

2

3.

-8

4.

18