# Show that $adj(adj(A)) = 0$

Let $n > 2$ and let $A$ be a real and singular (i.e., non-invertible) $n\times n$ matrix. Is it true that $adj(adj(A)) = 0$ ?

• A stronger result: see here or here. – user37238 Jan 29 '16 at 11:28

Hint : What is the adjugate matrix is the rank of A is strictly less than $n-1$? And what is the rank of $\text{adj}(A)$ when $\text{rk}(A)=n-1$?