expectation of sum (or square sum) of two matrices which entries are sampled from normal distribution

Question

Suppose we have two matrices, $A \in \mathbb{R}^{n \times k}$ and $B \in \mathbb{R}^{m \times k}$, and each entry of the matrices are sampled from $N(0, 1)$, I want to compute the expectation and variance of sum (and square sum) of all the entries in $AB^T$. But currently, I don't have any idea to compute the values.