If the product **A**_{n×m} **B**_{m×p} can be
formed, will it always be possible to form the product **B**_{m×p} **A**_{n×m}?

No. If n ≠ p then **BA** can't be formed. Later you will see that
even if both products can be formed, it is rare that **AB** = **BA**.

The matrix-matrix product **AB** is calculated by forming
the dot product of each row of **A** with each column of **B**.
Of course,
the number of columns in **A** equal to the number of rows in **B**.

As in the previous chapter,
flip a column of **B** so that its elements align with the
rows of **A**.
Form the dot product, which becomes row 1 col 1 of the result.
Now
slide down one row to form the next dot product,
which becomes row 2 col 1 of the result.
Continue down until the last row.

When you are finished with first column of **B**, move on to its
next column and do the same thing.
Continue with each column of **B** until all elements are calculated.

**Note:** Element ij of the result = dot product of row i
of **A** with column j of **B**.

Say that you are forming the product **A**_{ 5×3} **B**_{ 3×2} = **C**_{ 5×2}

What row and column are used to calculate the 3rd row 2nd column of **C** ?