We study applications of clustering (in particular the k-center clustering problem) in the design of efficient and practical deterministic algorithms for computing an approximate and the exact arithmetic matrix product of two 0-1 rectangular matrices A and B with clustered rows or columns, respectively. Let λA and λB denote the minimum maximum radius of a cluster in an ℓ-center clustering of the rows of A and in a k-center clustering of the columns of B,  respectively. In particular, when A and B are square matrices of size n×n, we obtain the following results. A simple deterministic algorithm that approximates each entry of the arithmetic matrix product of A and B within an additive error of at most 2λA in O(n2ℓ) time or at most 2λB in O(n2k) time.A simple deterministic preprocessing of the matrices A and B in O(n2ℓ) time or O(n2k) time after which every query asking for the exact value of an arbitrary entry of the arithmetic matrix product of A and B can be answered in O(λA) time or O(λB) time, respectively.A simple deterministic algorithm for the exact arithmetic matrix product of A and B running in time O(n2(ℓ+k+min{λA,λB})). A simple deterministic algorithm that approximates each entry of the arithmetic matrix product of A and B within an additive error of at most 2λA in O(n2ℓ) time or at most 2λB in O(n2k) time. A simple deterministic preprocessing of the matrices A and B in O(n2ℓ) time or O(n2k) time after which every query asking for the exact value of an arbitrary entry of the arithmetic matrix product of A and B can be answered in O(λA) time or O(λB) time, respectively. A simple deterministic algorithm for the exact arithmetic matrix product of A and B running in time O(n2(ℓ+k+min{λA,λB})).