Hello all, I don't have a question on homework specifically, but I need clarification on something I'm reading in the textbook. I will be starting an abstract algebra class in the spring and it's been quite a few years since I've had linear algebra, so I'll be reviewing that material before the abstract algebra class starts. I've also started the first chapter of the book, Algebra, by Michael Artin. So far, I've been able to make sense of most of what I've read, but I'm stuck on this one formula at the top of page 10. He states that the formulas for multiplying matrix units and standard basis vectors are: eijej = ei and eijek = 0 if j ≠ k I understand from the previous page that the matrix unit eij has a 1 in the ij position as its only non-zero entry and based on an example from the previous page, you can show a standard m x n matrix as a linear combination that includes eij. My confusion is in figuring out what the ei and ej are in the above formula. The bottom of the previous page discusses a column vector ei but I wasn't sure how to connect this vector to the above formula or how I should multiply it with eij to get ej. Maybe if I saw a couple of concrete examples of what ei and ej are as compared with eij, it would help me clear up this confusion. Thanks for any help on this question!