How to compute inverse of a matrix over finite field?

My guess is : Given $A$ a square matrix, then $A^{-1}=det(A)^{-1}adj(A)$ where $det(A)^{-1}$ is multiplication inverse of $det(A)$

• Your guess is correct: this algorithm works in any ring (whenever $\det A$ is invertible). – Crostul Apr 6 '17 at 7:12
• As spelled out in Hurkyl's answer (+1) the methods from a first course in linear algebra apply to any field. For a walkthru example of calculating the inverse of a 3x3 matrix over the field of 29 elements using elementary row operations see an old answer by yours truly. See also this. – Jyrki Lahtonen Apr 6 '17 at 7:19