With that lecture, you enter in the core of Scilab tutorial: the matrices, vectors and scalars global definition is explained. That topic is essential to use Scilab, and it is here explained in a very demonstrative way.
The "basic" operations are very basic in a way, as it is only addition and subtraction, but they are not so basic in another way, as they operate globally on matrices, rows vectors and column vectors as well as simply between numbers (scalars). So, do not bypass that part of the course, it is crucial to understand Scilab commands such as A+B!
A whole lecture is dedicated to multiplication, because this is a very important matter in Scilab. Indeed, the multiplication between two matrices, between a matrix and a vector or between two vectors is defined globally. The lecture shows also how to multiply two matrices or two vectors element by element, simply adding a dot before the star!
After the multiplation, we put variables to the power a number. We see in details how to put globally a square matrix to the square or to the power any integer or even, in some condition, non-integer numbers (square root for example). The lecture shows also how to put a matrix or a vector element by element to the power a number, and reversally. The operators are simply a hat ^ and a dot-hat .^.
Now, let's have fun, let's divide matrices ! This is a non-trivial issue, that is very easily done by Scilab. There are two operators, \ and /, for the left-hand and right-hand division. All this is clearly explained in the lecture.