Let $p$ be a prime number. Let $n \geq 2$ be an integer. Let $V$ be an $n$-dimensional $\mathbb { F } _ { p }$-vector space. Determine, with a proof, the number of two-dimensional $\mathbb { F } _ { p }$-subspaces of $V$.
Let $p$ be a prime number. Let $n \geq 2$ be an integer. Let $V$ be an $n$-dimensional $\mathbb { F } _ { p }$-vector space. Determine, with a proof, the number of two-dimensional $\mathbb { F } _ { p }$-subspaces of $V$.