The Strassen algorithm is a divide-and-conquer algorithm for multiplying two by matrices, where is a power of two. Similar to the Karatsuba trick, this gives a speedup on the brute force method for multiplying matrices, and its analysis follows similarly. Here, we use the Master Theorem to explicitly give a time bound on the Strassen algorithm.

Given two matrices and , we first split them each into 4 smaller square matrices, as follows.

and 

What are the dimensions of each of the matrices ?