Let X = (X 1 , ...,X k ) be a random vector with a covariance matrix

Question:

Let X = (X₁, ...,X_k) be a random vector with a covariance matrix C, and t = (t₁, ..., t_k) and ˜t= (˜t₁, ..., ˜t_k) be two non-random vectors. Consider two linear combinations: 〈X, t〉 and 〈X,˜t〉. Generalizing (2.1.4), prove that Cov{〈X, t〉, 〈X,˜t〉} = 〈Ct,˜t〉. Can we switch t and˜t in the r.-h.s. of this formula? Why?