Why matrix multipliucation is possible by row vs column?

Matrix multiplication is possible by row versus column because it involves taking the dot product of the rows of the first matrix with the columns of the second matrix. Each element of the resulting matrix is computed by summing the products of corresponding entries from a row of the first matrix and a column of the second matrix. This operation aligns with the definition of matrix multiplication, where the number of columns in the first matrix must equal the number of rows in the second matrix. Thus, the row-column pairing enables systematic computation of the resulting matrix's elements.