My guess that you used multiply instead of Dot (which is an inner product).
In[11]:= ii = IdentityMatrix[3];
In[10]:= m = {{2, 2, 3}, {4, 5, 6}, {1, 2, 3}}
In[17]:= ans = m . ii
Out[17]= {{2, 2, 3}, {4, 5, 6}, {1, 2, 3}}
Does this fix your discrepancy?
Regards