Question

Prove that if an nxn matric A is not invertible, then A[adj(A)] is the zero matrix

Answer 1

\[\mathbf{A} adj(\mathbf{A} ) = \det(A)\mathbf{I} \]
Where I is the identity matrix. I don't know how to relate the above to the way of expression the adjugate using minors, but if you take this to be true, the proof is simple.
What is the determinant of a non-invertible matrix?