1. The problem is to find the product of $-1$ and $-2$. 2. The rule for multiplying integers states that the product of two numbers with the same sign is positive. 3. Since both $-1$ and $-2$ are negative, their product will be positive. 4. Multiply the absolute values: $1 \times 2 = 2$. 5. Therefore, $-1 \times -2 = 2$. The final answer is $2$.