Say I have an elementary matrix associated with a row operation performed when doing Jordan Gaussian elimination so for example if I took the matrix that added 3 times the 1st row and added it to the 3rd row then the matrix would be the $3\times3$ identity matrix with a $3$ in the first column 3rd row instead of a zero.
Is there a way to quickly determine it's inverse (as in just by looking at it pretty much and without calculating cofactor matrix and transposing it.)
Thanks.
The inverses of elementary matrices are described in the properties section of the wikipedia page