To multiply matrices, always multiply a row of the left matrix with a column of the right matrix. It helps to picture the column of the second matrix “flying out” of its matrix and hovering over the row of the first matrix, so you can do the multiplication quickly and easily.
Example:
Let’s say you are going to multiply the first row of the first matrix by the second column of the second matrix:
In your mind, place the column over the row to line up the corresponding elements:
Then you can quickly calculate (1 · 2) + (-4 · 3) + (2 · 4) = -2.