My guess is : Given $A$ a square matrix, then $A^{-1}=det(A)^{-1}adj(A)$ where $det(A)^{-1}$ is multiplication inverse of $det(A)$
2026-04-04 22:20:35.1775341235
How to compute inverse of a matrix over finite field?
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Most likely, whatever algorithms you would use to find the inverse of an invertible real matrix will work completely unchanged to find the inverse of an invertible matrix over any field. And the reason why they work will be similarly unchanged.
(I say "most likely" because there do exist some algorithms for doing matrix operations that depend somewhat on the field... but it's very unlikely that you would consider using them)
The formula you wrote is true, but its mainly meant for theoretical reasoning, not for doing computation.