Construct a $3\times 3$ nonsingular matrix and call it $A$. Then, for each entry of the matrix, compute the corresponding cofactor, and create a new $3\times 3$ matrix full of these cofactors by placing the cofactor of an entry in the same location as the entry it was based on. Once complete, call this matrix $C$. Compute $A\transpose{C}$. Any observations? Repeat with a new matrix, or perhaps with a $4\times 4$ matrix.