Linear Algebra: A Modern Introduction

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We're asked to simplify $3+1+2+3$ in $\mathbb{Z}_4$. Using the associative property repeatedly, we can group this into the following form: $$(((3+1)+2)+3)$$ Now, knowing the addition table for $\mathbb{Z}_4$, we simplify: $$((0+2)+3)=((2)+3)=1$$