Strassen's matrix multiplication algorithm when $n$ is not a power of 2

The above image, describing Strassen's matrix multiplication algorithm, is from the book Introduction to Algorithms by Cormen, Leiserson, Rivest, and Stein.
The algorithm multiplies two square matrices of order $n$, where $n$ is a power of $2$, i.e., $n=2,4,8,16,32,\dots$ and so on.


Can this algorithm be modified so that we can multiply two square matrices of order $n$, for all $n$?

The solution is to pad the matrices with zeroes, using the block matrix identity
$$
\begin{bmatrix}
A & 0 \\
0 & 0
\end{bmatrix}
\begin{bmatrix}
B & 0 \\
0 & 0
\end{bmatrix}
=
\begin{bmatrix}
AB & 0 \\
0 & 0
\end{bmatrix}
.
$$

Here $A,B$ are $n\times n$ matrices, and the big matrices are $N\times N$ for some $N > n$. In other words, we add $N-n$ rows and $N-n$ columns of zeroes.

You can do this in two ways:

-
Pad the original $n \times n$ matrices to $N \times N$ matrices, where $N$ is the closest power of 2. Note that $N

-
Pad the matrices recursively. Whenever a recursive call gets $m \times m$ matrices with $m > 1$ odd, we pad them to $(m+1) \times (m+1)$ matrices by adding a single row and a single column of zeroes. This also doesn't affect the asymptotic complexity.

A third option is to make use of, say, a 3x3 matrix multiplication algorithm if the dimension is odd but divisible by 3. Laderman found such an algorithm which uses 23 multiplications (instead of the trivial 27).

StackExchange Computer Science Q#97998, answer score: 3