"Manipulating" Normal Distributions

Question

I am reading the following book https://algorithmsbook.com/optimization/files/optimization.pdf at page 281:

I am trying to understand how to manipulate the matrix terms to verify the following 2 relations:

My Question: Can someone please show me how to verify that 1) and 2) are true? How can I manipulate the matrix terms within the Normal Distributions (within the Gaussian Process) to verify 1) and 2)?

Thanks!