We have $N\times N$ matrices A, B and C and we wish to evaluate $A=BC$. $$\mathbf{A}=\mathbf{BC} \Longrightarrow a_{ij} = \sum_{k=1}^{n} b_{ik}c_{kj},$$ In C/C++ this would be coded like

   for(i=0 ; i < N ; i++) {
      for(j=0 ; j < N ; j++) {
         for(k=0 ; k < N ; k++) {
            a[i][j]+=b[i][k]*c[k][j];