Welcome back, last time we were talking about matrix algebra. We were talking about adding two matrices and we did an example of that. This time we're going to come back, and we're going to talk about scale. Or else, we're going to talk about the identity matrix. Now, the identity matrix is a very nice matrix, in which multiplying another matrix by the identity matrix will keep the original matrix the same, okay? It's the same as 1, when it comes to multiplying other numbers. If you have 4, you multiply by 1, you get the original 4 back. If we have a matrix and we multiply by the identity matrix, we get the original matrix back. We're going to see how that is, and that deals with multiplication. So, today we're just talking about the concept of an identity matrix. Will need to cover how matrix multiplication works. And then we can see an example of how the identity matrix actually works. So, the concept again, of the identity matrix is just a matrix when you multiply by another matrix. It keeps the original matrix in its original form. So, let's talk about scale, and for scale, it's kind of the same as pretty much original algebra, okay? If you wanted to multiply a number, let's say, 4.2, we just get 8, okay? It's the same exact thing, when it comes to a matrix. 2 times of matrix, it's just 2 times all entries, Of A, simple as that. And we can do this with any matrix, you can scale any matrix out there. So, let's say, we have A is 2 x 2 matrix, -1, 1, 7, square root of 3. And what we want is, let's say, 2.A. This is what we want. The scale is just going to be like normal algebra, you're going to take the 2 here and multiplied by each entry in A. So 2 times A, will just be -1 times 2 is -2. 1 times 2 is 2. 7 times 2 is 14. Square root of 3 times 2 is 2 times the square root of 3. Simple as that. So, when we scale the matrix, we simply take each entry of the matrix. We multiply it by the scale, whatever constant we're trying to introduce into this matrix, and we get a resulting matrix. The resulting matrix, keep in mind, will be the same dimension as the original matrix. So, this A was a 2 x 2. This 2A, which we can call C, is also a 2 x 2. So, we've covered scale now. We've covered, [COUGH] the addition of 2 matrices. We've covered the concept of what an identity matrix does in practice. Next lesson, let's cover matrix multiplication. Again, it gets a little bit more complicated. And then we can introduce the identity matrix and actually do an example of that as well.