In this paper we describe a complete solution for the first challenge of the VerifyThis 2016 competition held at the 18th ETAPS Forum. We present the proof of two variants for the multiplication of matrices: a naive version using three nested loops and the Strassen's algorithm. The proofs are conducted using the Why3 platform for deductive program verification, and automated theorem provers to discharge proof obligations. In order to specify and prove the two multiplication algorithms , we develop a new Why3 theory of matrices and apply the proof by reflection methodology.