[maze-le]

I have just asked it the following: Suppose we have the set of all n x n Matrices denoted as M(n,n). Further we define the operation ・ as Matrix multiplication. Is G=(M(n,n),・) a group?

It incorrectly stated that G is a group and has given me the list of group axioms that must be satisfied. Since not all n x n Matrices do necessarily have an inverse G is not a group. So this answer was wrong and I've "explained" why.

2 hours later I've asked the very same question again (with a slightly different wording) in a completely new session. It not only has given me the correct answer it also deduced why G is not a group and how the set M(n,n) can be restricted to only include Matrices with non zero determinant, so that G becomes a group.

That pretty impressive!