# Fastest way to find inverse of 4x4 matrix?

What is the fastest way to find the inverse of a 4x4 matrix?

The only way I know is to set up the matrix with the 4x4 matrix and the identity matrix and row reduce. But that takes forever sometimes.

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gabbagabbahey
Homework Helper
Gold Member
What is the fastest way to find the inverse of a 4x4 matrix?

The only way I know is to set up the matrix with the 4x4 matrix and the identity matrix and row reduce. But that takes forever sometimes.
It is often (but not always) faster to use the determinant and the adjugate matrix.

Ray Vickson
Homework Helper
Dearly Missed
It is often (but not always) faster to use the determinant and the adjugate matrix.
It is hardly ever faster to use determinants. You would need to calculate 16 determinants, each of which is 3x3, so each involves 9 three-factor multiplications, plus keeping track of signs and worrying about roundoff error effects. Direct row-reduction is likely much faster in the vast majority of cases. And, yes, it can involve a lot of work, but that's life!

RGV

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