What is the key property of a matrix required for matrix addition to be valid?

Matrix addition requires that both matrices involved have the same dimensions because this ensures that each corresponding element can be added together. Specifically, if one matrix has a size of m x n (m rows and n columns), the other matrix must also be of size m x n. This alignment allows for each element at position (i, j) in the first matrix to be matched with the element at the same position in the second matrix for the addition operation.

If the matrices do not have the same dimensions, there would be no matching elements to perform the addition, making it mathematically invalid. Hence, the key property for matrix addition is having matching dimensions, as this preserves the structural integrity of the operation across all elements involved.