iid matrix distribution

[carmine rock]

can anyone help me with how to start part a of this question?

[stuck pebble]

Basically $Y_i=A_{ij}X_j$ (summation convention applies, so we're summing over $j$) This gives you a sum of independent normal random variables. Then, you can use, for example, moment generating function to show that $Y_i$ is normal with some mean and variance.