How much can matrix multiplication algorithm be parallelized?
Ypu're starting from a completely wrong point. 

The execution time of matrix multiplication does not come from the number of multiplications and additions, it's the number of uncached memory accesses that kill you. Reading a number that's not in any processor cache takes about 100 times longer than a multiplication. 

So the first step is rearranging the order of operations to perform as many operations as possible using only data that is present in the fastest processor cache. That's your first step before you even think about doing things in parallel. 

The next step is adding multiple sums in parallel, still in one thread. Instead of summing up C[i,j] for example you add six sums C[i, j], C[i,j+1], C[i, j+2], C[i+1, j], C[i+1,j+1], C[i+1, j+2] in parallel. This means you are limited by the throughput of operations, not the latency. 

The next step is using SIMD instructions. Your processor quite likely has instructions that perform 2, 4 or 8 floating-point operations just as fast as a single floating-point operation. 

Once you have done all this, especially the first part where the work is divided up into "blocks", you can easily process multiple blocks on multiple threads. What you need to be careful about is that you have enough cache memory to do so.