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?
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.
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?
Yes. He just proved that the inverse of AB is B^(-1)A^(-1).
is not abelian, since 0 does not exist an inverse.
Around 1:20 I was convinced he was going to call a can of soup abelian
Or 1,000 times 1,000,000
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.
I can't find a place in the video where he includes the matrix (0 0) (0 1)
+learnifyable can yu explain what yu mean by the 7th & 8th(last 2 on 2nd column) groups being abelian?! Don't get that notation
great explanation thanks sir
Isn't the fifth Abelian group communicative? Closure, associative, identity, inverse and...?
What do you mean by fifth?
amazing video thank you so much!
Thanks
Do we have a billion abilian? XD