Given N matrices A1, A2, ..., AN of size N X N, the matrix chain product problem is to compute A1 X A2 X … X AN. Given an N X N matrix A, the matrix powers problem is to calculate the first N powers of A, i.e., A, A2, A3, ..., AN. We show that the two problems can be solved in and times respectively, where a < 2.3755, and p, the number of processors, can be arbitrarily chosen in the interval [1..Nα+1]. Our highly scalable algorithms can be implemented on a linear array with a reconfigurable pipelined bus system, which is a distributed memory system using optical interconnections.