00:01
If we have a square matrix, say m with the elements a, b, c, d, the inverse of m, which we denote as m to the negative 1, is a matrix such that m times the inverse will give us the identity matrix.
00:17
So when we're trying to find the inverse of a two -by -two matrix, the first step we need to do is to calculate something called the determinant of the matrix.
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Determinant is denoted by these bars with the letter of the matrix inside.
00:35
And it's defined to be the product of this main diagonal minus the product of this b and c.
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So let's take a look at how to find the inverse of a couple of different matrices.
00:50
So let's start with, let's say, matrix a, which is 7, 5, 3.
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The first thing we want to do is to evaluate the determinant of a.
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So remember that is the product of the main diagonal, 7 times 3, minus this product here, 4 times 5.
01:15
And that would give us 21 minus 20, which is 1.
01:19
Now the way that we calculate the inverse of a is we multiply a or some iteration of a, by the reciprocal of our determinant, which is, so this would be one over one.
01:38
And what we're multiplying it to is we take these elements on the main diagonal and we interchange them.
01:45
So this would be the three up here and the seven comes down here.
01:49
And then for these other two, we're going to take the negative of them.
01:53
So this would be a negative four and a negative five.
01:58
So that is just the inverse there, three, negative four, negative 5, 7.
02:07
Let's consider matrix b, which has the elements, 2, 3, 4, 5.
02:18
So first figuring out the determinant, which again is the product of the elements in the main diagonal, 2 times 5, minus the product of these elements, 3 times 4.
02:33
So 10 minus 12 is is negative 2...