But that is sort of the point. In theory, it's the same. But that's not how you should actually compute it. The cheap way is to compute 21/7. The hard way is

But that is sort of the point. In theory, it's the same. But that's not how you should actually compute it. The cheap way is to compute 21/7. The hard way is to compute 1/7 (one floating point operation), and then multiply it by 21 (another floating point operation). With matrices, the discrepancy in work and possibly precision between "solve Ax=b" and "compute x = A^-1 b" can be very large.