Let X be a kn $\backslash$times n matrix and Y be an n $\backslash$times kn matrix, for some integer k $>0.$

$($a$)$ Describe an algorithm which computes the product XY by making calls to Strassen$$s algorithm.

$($Treat Strassen$$s algorithm as a black$-$box and do not modify it; just issue calls to it$.$ You should

not delve into its inner workings.$)$

A careful answer, in words, suffices; pseudocode is not required. Argue briefly that your algorithm

does compute XY and establish its running time.

Note: Avoid padding the matrices with zeros to make them square, as this will lead to an inefficient

solution.

$($b$)$ Re$-$do the problem above, this time computing the product Y X$.$