Multiplications in determinant of an $n \times n$ matrix?

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Assuming we use Gaussian Elimination/LU decomp, is there a general formula to describe the number of multiplications involved in finding the determinant of an $N \times N$ matrix?

Find the computational cost associated with calculating determinant of an $n\times n$?

I stumbled upon what I believed to be the correct answer above, but just wanted to clarify, when it says $M(n) = \mathcal{O}(N^3)$ this means the number of multiplications is $N^3$? Or have I mis-interpreted the answer?