Diagonal Shortcut

Let $A = \text{diag}(a_1, \ldots, a_n)$ be a diagonal matrix. How do the quadratic form $x^\top A x$ and $\det(A)$ simplify?

$x^\top A x = \prod_i a_i x_i^2$ , and $\det(A) = \sum_i a_i$

$x^\top A x = \sum_i a_i x_i^2$ , and $\det(A) = \prod_i a_i$

$x^\top A x = \sum_i a_i x_i$ , and $\det(A) = \sum_i a_i$

$x^\top A x = \left(\sum_i a_i\right)\left(\sum_i x_i^2\right)$ , and $\det(A) = \prod_i a_i$