For example If I was doing row reduction to an augmented matrix to find a solution or something, I could just plug the unknowns into one of the smallest equation of the linear system to see if its correct (99.9% this would work, well has worked for me thus far). For inverse how would I check? (This is for test purposes so like it doesn't take up too much time).
$\endgroup$ 41 Answer
$\begingroup$You started with a matrix $A$ (whose determinant is non-zero). You've calculated a matrix $B$ which you claim is equal to $A^{-1}.$ To check, just calculate $AB$ and make sure it's equal to the identity matrix.
True, this takes about $n^{3}$ operations to do by hand, for an $n\times n$ matrix, but it's basically fool-proof, and if you're calculating the inverse by hand then $n$ can only be as large as $3$ or $4.$
$\endgroup$ 5
