1)Is the set of invertible 2x2 matrices having real entries with matrix multiplication and with scalar multiplication vector space?
2)Is the set of invertible 2x2 matrices having real entries with matrix addition and with scalar multiplication vector space?
I don't quite understand question 1), does it mean vector addition a+b is defined by a.b? And what is the difference between the 2 questions?
Recall that for a subspace all the following three properties must be satisfied:
1) $\vec{0} \in W$
2) $\vec{v}+\vec{w} \in W$
3) $\vec{cv}\to c \cdot \vec{v} \ ,c \in \mathbb{R}$
but this is not a subspace since $$\vec{0}\notin W$$