Past exam of the mathematics course of the University of Cambridge / 2019 / ia / Paper 2 / 11F / a / i / Solution

For every $u\in {\mathbb{R}}^2$,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 $\boxed{AX\text{ is bivariate normal}}$.