LTI systems inverse of each other
So you have
$$
\int_{-\infty}^{+\infty} \delta(u) \delta(t-u) du
$$

Try using the sifting property of $\delta(t)$:

$$
\int_{-\infty}^{+\infty} f(u) \delta(T-u) du = f(T)
$$