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STD 12 - 3 and 4 . determinant and metrices — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 3 and 4 . determinant and metrices4 Marks
MCQ
If $P\left( \theta  \right) = \left[ {\begin{array}{*{20}{c}}  1&{\cot \theta } \\   { - \cot \theta }&1 \end{array}} \right]$ and $PQ$ = $I$, then $\left( {\cos e{c^2}\theta } \right)Q$  (where $I$ is an identity matrix of $2×2$ order)
  • A
    $P\left( \theta  \right)$
  • ✓
    $P\left( { - \theta } \right)$
  • C
    $P\left( {2\theta } \right)$
  • D
    $I$
✓

Answer

Correct option: B.
$P\left( { - \theta } \right)$
b
$Q = {P^{ - 1}} = \frac{{\left[ {\begin{array}{*{20}{c}}
1&{ - \cot \theta }\\
{\cot \theta }&1
\end{array}} \right]}}{{\cos e{c^2}\theta }}$

$\therefore {\rm{Q}}cose{c^2}\theta  = {\rm{P}}( - \theta )$

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