It's going to be 2, 1, 1, 1.

What is this thing right here?

So B inverse is going to be equal to 1 over the determinant of B.

It's just a little tedious.

It's the determinant.

Let's calculate B inverse.

We go back to plus.

So the inverse of matrix a is equal to 1 over the determinant of a times the adjugate, or adjoint, of matrix a.

But what is this?

But that is a really neat outcome.

But we're ready now to solve the inverse of a.

So the area of your parallelogram squared is equal to the determinant of the matrix whose column vectors construct that parallelogram.

learned from Wikipedia, the correct term is the adjugate of matrix a.

So now let's solve for the determinant.

Well you cross out row 1, column 3.

You have plus, and then you go minus.

Cross out the first row, first column, I want the determinant of this thing right here.

So another way of saying this, this could be 1 over the determinant.

This is the determinant of my matrix.

And then I will take the determinant so when I go to this position, I'm in row 1, column 2.

left with this 0, this 1, this 1, and this 1.

And actually maybe I'll write that down.

And what it is, so this element, this top left element, is essentially going to be the determinant.

One possibility for how you can evaluate again like this is just to convert it to the other form.

Remember, all I did is, I said, OK, in position 1,1, let me cross out the column and the row 1,1, and take the determinant of what's left.

Or the minor of this matrix.

So this is minus 1 7.

I have this right here.

So 0 times 1 is 0, minus 1 times 1 is minus 1.

Function MDETERM returns the determinant of a given matrix. The matrix must be of type n x n.

But anyway, let's go back to this position 1, 1.

So the inverse of a is equal to 1 over the determinant.

Well it's just 1.

Right?

In future videos, I promise to give you more tuition.

We figured out the determinant is negative 1 times the adjugate of a.

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So minus c minus b.

Just one more sort of, tricky thing in matrix algebra, and then we'll go on to a sort of cool example.

And this quantity down here, ad minus bc, that's called the determinant of the matrix A.

I think they actually teach this in Algebra 2 you could at least, if the teacher asks you, solve for the matrix of minors or the cofactors or solve for the determinant of the inverse, you can do it.

You also have a rotation matrix that will rotate the model or anything else around the y axis.

That is the determinant of my matrix A, my original matrix that I started the problem with, which is equal to the determinant of abcd.

So what is this?

So we solved for this part.