In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring. The ma
In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring. The matrix product is designed for representing the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, physics, and engineering. In more detail, if A is an n x m matrix and B is an m x p matrix, their product AB is an n x p matrix, in which the m entries across a row of A are multiplied with the m emtries down a column of B and summed to produce an entry of AB. When two linear maps are represented by matrices, then the matrix product represents the composition of the two maps. We can only multiply two matrices if their dimensions are compatible, which means the number of columns in the first matrix is the same as the number of rows in the second matrix. If A is an n x m matrix and B is an m x p matrix, the matrix product C = AB is defined to be the n x p matrix such that cij=∑k=1maikbkjc_{ij} = sum_{k=1}^{m} a_{ik} b_{kj}cij=∑k=1maikbkj, for i = 1,2, ..., n and j = 1,2, ..., p. Your task is to design a matrix multiplication calculator to multiply two matrices and display the output. If the matrices cannot be multiplied, display "ERROR".
