(Abstract Algebra 1) Definition of an Abelian Group

A definition of an abelian group is provided along with examples using matrix groups. The general linear group and the special linear group are introduced.

[ianiceman]

For closure, I thought you had to show if A and B are in G, then AB is also in G?
then can't you say that det A and det B are non zero, so det(AB)=det(A) det (B), which is non zero, so AB is invertible, which means AB is also in G?

[hamiyed]

The set of all nxn matrices with real entries under matrix multiplication. There you have said that the multiplication of (0 0) (1 0) should give the identity matrix. Actually matrix
(0 0) (0 1) AI = A so there is no problem with that. where I is identity matrix. If am wrong plz correct me.

[NotOnlyMagicMan]

Around 1:20 I was convinced he was going to call a can of soup abelian

[sinethembamkhize]

+learnifyable can yu explain what yu mean by the 7th & 8th(last 2 on 2nd column) groups being abelian?! Don't get that notation

[lulualita]

<R, ·> is not abelian, since 0 does not exist an inverse.

[robertadorrough]

Isn't the fifth Abelian group communicative? Closure, associative, identity, inverse and...?