$A=\left[\begin{array}{cccc}2& 3& 1& -2\\ 5& 3& 6& -1\\ 1& 3& 2& 2\\ 0& 4& 1& 2\end{array}\right],B=\left[\begin{array}{cccc}-1& 3& 2& 1\\ 4& 2& -3& 1\\ 1& 0& 3& 2\\ 2& -2& 1& 4\end{array}\right]$

Show your work in detail $-$ yes, this will be extremely tedious. $($Careful bookkeeping is the key.

Don't use any "shortcuts" on the $22$ multiplications, do them by Strassen's algorithm as well.

And remember that you have a check on the correct matrix results as you go along by just doing

ordinary matrix multiplication.$)$ Compute the total number of additions and the total number

of multiplications of array elements $($numbers$)$ done in this process. Compare these results

with the exact expressions we derived for multiplications and additions using Strassen's

algorithm. Also compare these results with the work to use standard matrix multiplication.