What is required for matrix multiplication to be possible?

Matrix multiplication can only occur under specific conditions related to the dimensions of the matrices involved. For two matrices to be multiplied, the number of columns in the first matrix must match the number of rows in the second matrix.

This requirement exists because each entry in the resulting matrix is computed by taking the dot product of a row from the first matrix and a column from the second matrix. Therefore, if the number of columns in the first matrix did not equal the number of rows in the second, it would be impossible to perform this operation meaningfully. Each entry of the resulting matrix corresponds to the sum of products of elements, which relies on having a matching number of elements available to multiply.

The other options suggest different requirements for matrix multiplication, but they do not accurately describe the fundamental rule. For instance, while it might seem that matrices of the same size or both being square could potentially allow multiplication, those conditions do not specifically address the necessary dimensional compatibility that allows for the dot product computations inherent in matrix multiplication.