1. The problem asks if $-1$ is a self multiplicative inverse. 2. A number $a$ is a self multiplicative inverse if $a \times a = 1$. 3. We test this for $-1$ by calculating $(-1) \times (-1)$. 4. Multiplying, we get $$(-1) \times (-1) = 1$$ 5. Since the product is $1$, $-1$ is indeed a self multiplicative inverse. 6. Therefore, the answer is yes, $-1$ is a self multiplicative inverse.