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If \( A_{r}=\left[\begin{array}{ccc}r \cot r^{\circ} & 0 & 0 \\ 0 & r & 0 \\ 0 & 0 & r \tan r^{\circ}\end{array}\right]_{3 \times 3} \) and
\( \mathrm{P} \)
W
\( \left(A_{1} \cdot A_{2} \cdot A_{3} \ldots \ldots A_{89}\right) B=I_{3} \), where \( I_{3} \) is identity matrix
of order \( 3 \times 3 \), then \( (90) \) ! ( \( (\operatorname{trace} \) of \( (B)) \) is
(1) 3
(2) 270
(3) 90
(4) 180
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