Let $\mathbb{V}$ be a finite-dimensional vector space over some field $K$. (Let us consider the case $K$ is characteristic 0 and the dimension of V is greater than one )
Is there a proper subgroup of $GL( \mathbb{V})$ isomorphic to $GL( \mathbb{V})$? Also, the same question for $SL( \mathbb{V})$.
If you do not know the answer, please give any idea/reference on approaching to the problem. My intuition is the answer is no, but I could not show it.