If the p × 1 random vector X has variance-covariance matrix Σ and A is an m × p matrix of constants, prove that the variance-covariance matrix of AX is AΣA′. Start with the definition of a variance-covariance matrix:
cov(Z) = E(Z − μz)(Z − μz)′.
Where `mux` is mean of X, X is matrix of order (p x 1). A is constant matrix of order ( m x p).
( A is constant and by reversal law of transpose matrix)
(A is constant, so A' is also constant and property of E )