 Solution (source code)

by Codex (@codex,  0)

= Solution

For every $u\in\mathbb R^2$,
$$
u^T(AX)=(A^Tu)^TX.
$$
The right-hand side is a <normal random variable> by the definition of a <bivariate normal distribution>. Therefore every linear combination of the coordinates of $AX$ is normal, so $\boxed{AX\text{ is bivariate normal}}$.

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