Matrix Multiplication

Suppose you are multiplying a $m\times n$ matrix with a $p\times q$ matrix.

1. Determine if the multiplication is well-defined. The number of columns of the first (left) matrix must be equal to the number of row of the second (right) matrix. Stated simply, $n = p$.
2. Find the dot product of rows in the first matrix to columns in the second matrix.
3. The result should be of the dimension $m\times q$.