Answer
No pair of diagonals are perpendicular.
Work Step by Step
We need to prove that any pair of diagonals are not perpendicular.That is, the dot product of any pair of diagonals must be non-zero.
Thus, $d_1 \cdot d_2= 1+1-1=1$; $d_1 \cdot d_3= 1-1-1=-1$;$d_1 \cdot d_4= -1+1-1=-1$;$d_2 \cdot d_3= 1-1+1=1$; $d_2 \cdot d_4= -1+1+1=1$; and $d_3 \cdot d_4= -1-1+1=-1$;
The dot product of any pair of diagonals is non-zero, so no pair of diagonals are perpendicular.
