How many recursive calls need to be made so that the

Question

Question :

Suppose that we want to create a divide and conquer matrix multiplication algorithm for square matrices.

Assuming that n is a power of three, the algorithm divides each matrix of A, D, and C into nine equi-sized matrices. Then, it performs some recursive calls to compute each submatrix of c.

How many recursive calls need to be made so that the algorithm will have an asymptotic running time of Theta (n³)?

What is the maximum number of recursive calls that can be made while having an asymptotic running time that is lower than that of Strassen's algorithm?