Let K {\displaystyle {}K} denote a field, and let A {\displaystyle {}A} denote an m × n {\displaystyle {}m\times n} -matrix and B {\displaystyle {}B} an n × p {\displaystyle {}n\times p} -matrix over K {\displaystyle {}K} . Then the matrix product
is the m × p {\displaystyle {}m\times p} -matrix, whose entries are given by
