Determine whether the given set of invertible n x n matrices with real number entries is a subgroup of $GL(n,\mathbb{R})$
The n x n matrices with determinant 2
The key said
I understand that's how you compute determinants, but why did they pick out multiplication? Why couldn't they say for instance
"If detA = detB = 2, then we also see that detA + detB = 4 and it is not closed under addition".