00:01
If we have a square matrix, say like m, the inverse of m is denoted by m to the negative 1.
00:09
And this inverse is such that when you multiply the matrix times its inverse, you get the identity matrix.
00:18
Now, one step in finding the inverse of a matrix is to calculate something called the determinant of the matrix.
00:25
So in a two -by -two matrix, we have the elements in the row a, b, and then c -d.
00:31
The determinant, which is denoted as kind of looks like an absolute value, but it's not, of m equals multiply the a and the d and subtract the product of b times c.
00:45
So let's find the determinant of a matrix and then go through the steps of how to find its inverse.
00:51
So let's say, for example, i have a matrix a with the elements 5, 3, 4, 2.
00:59
Then the determinant of a would be this product down the main diagonal, 5 times 2, minus this product of 3 times 4.
01:14
So that would give me 10 minus 12, which is a negative 2.
01:19
To find the inverse of a, what we're going to do is to multiply 1 over negative 2.
01:29
So we're going to multiply by 1 over the determinant.
01:33
And we're going to multiply by switching the numbers on the main diagonal.
01:42
So this would be a 2 and a 5.
01:45
And then taking the negative of these other two elements, negative 3, negative 4.
01:53
And then doing that scalar multiplication, so we would have negative 1, positive 3, three halves, positive two, negative five halves.
02:05
Let's try another example...