## Linear Algebra: A Modern Introduction

$$1$$
We're given the following, in $\mathbb{Z}_3$: $$2(2+1+2)$$ First, using the associativity of addition, group the terms: $$2((2+1)+2)$$ Given that $2+1=0$ in $\mathbb{Z}_3$, we can simplify it to: $$2(0+2)$$ Using the identity property of addition, this simplifies to: $$2(2)$$ And computing the product, we get: $$1$$