How many rows and columns must the matrix $$M$$ have in order to be able to do the product: $$\left( \begin{array}{cc} 2 & 1 \\ 3 & 4 \\ 1 & 5 \end{array} \right)\cdot M$$
And if the product is $$M \cdot \left( \begin{array}{cc} 2 & 1 \\ 3 & 4 \\ 1 & 5 \end{array} \right)$$
Development:
As the first matrix has $$3$$ rows and $$2$$ columns, the second must have $$2$$ rows and $$3$$ columns. The result of the product will be a matrix with $$3$$ rows and $$3$$ columns.
In the second case, where $$M$$ is in front and it is the first factor, it must also have $$2$$ rows and $$3$$ columns. Nevertheless, the result of the multiplication will be a matrix with $$2$$ rows and $$2$$ columns.
Solution:
In both cases $$M$$ should be a $$2\times3$$ matrix.