the question below

Pr. 2. (a) Prove the "vec trick," i.e., that for arbitrary (possibly complex-valued) matrices of compatible sizes: vec(AXBT) = (B @ A) vec(X), (1) where vec(.) is the operator that stacks the columns of the input matrix into a vector, and & denotes the Kronecker product. Note that here we really mean transpose B' even if B is complex valued! For your solution, use: A is p x m, X ism x n, and B is q x n. (b) Suppose A, X, and B are all N X N dense matrices. Determine how many scalar multiplications are needed for the LHS vec(AXB' ) and compare to the number for the RHS (B O A) vec(X). Which version uses fewer multiplications