Answer
$(1,1)\cdot(1,-1)=0$
Work Step by Step
If the vectors are perpendicular, their dot product must be zero.
Dot product$=(1,1)\cdot(1,-1)=1(1)+1(-1)=1-1=0$.
Therefore, $\textbf {i}+\textbf {j}$ and $\textbf {i}-\textbf {j}$ are perpendicular.