When we multiply a matrix by a scalar (i.e., a single number) we simply multiply all the matrix's terms by that scalar. We can also multiply a matrix by another matrix, but this process is more complicated. …

Learn about the properties of matrix multiplication (like the distributive property) and how they relate to real number multiplication.

We're going to be taking the dot product of this first row and this first column to get this top left entry right over here. If the word "dot product" makes no sense to you, I will show you what that actually means.

So you're not just blindly doing some-- matrix-matrix products can be pretty tedious, but now you know what they're for. They're actually for the composition of two transformations where each of A and B …

Learn about the conditions for matrix multiplication to be defined, and about the dimensions of the product of two matrices.

You can think of a point in three dimensional space as a 1 by 3 matrix, where the x coordinate is the 1,1 value in the matrix, y is the 1,2 and the z coordinate is the 1,3 value.

Learn about the dot product and how it measures the relative direction of two vectors.

The identity matrix plays a similar role in operations with matrices as the number 1 plays in operations with real numbers. Let's take a look.

You can't. When you take a dot product, it converts two vectors into a scalar. Attempting another dot product after that is impossible, because you would be trying to dot a scalar with a vector, which …

The dot product of those column vectors, each of the corresponding column vectors, with your matrix X. So these are both completely valid interpretations, and hopefully this video at least gives you a …