If A = [ * 20 c ^2 & & ^2 ], B = [ * 20 c ^2 & & ^2 ] and and differs by 2 , then AB =

If A = [ * 20 c ^2 & & ^2 ], B = [ * 20 c ^2 & & ^2 ] and and dif…

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}{{{\cos }^2}\theta }&{\sin \theta \cos \theta }\\{\sin \theta \cos \theta }&{{{\sin }^2}\theta }\end{array}} \right]$, $B = \left[ {\begin{array}{*{20}{c}}{{{\cos }^2}\phi }&{\sin \phi \cos \phi }\\{\sin \phi \cos \phi }&{{{\sin }^2}\phi }\end{array}} \right]$ and $\theta $ and $\phi $ differs by $\frac{\pi }{2},$ then $AB = $

A
$I$
✓
$O$
C
$-I$
D
None of these

✓

Answer

Correct option: B.

$O$

b
(b) $AB = \left[ {\begin{array}{*{20}{c}}{{{\cos }^2}\theta }&{\sin \theta \cos \theta }\\{\sin \theta \cos \theta }&{{{\sin }^2}\theta }\end{array}} \right]\,\,\left[ {\begin{array}{*{20}{c}}{{{\cos }^2}\phi }&{\sin \phi \cos \phi }\\{\sin \phi \cos \phi }&{{{\sin }^2}\phi }\end{array}} \right]$
= $\left[ {\begin{array}{*{20}{c}}{\cos \theta \cos \phi \cos (\theta - \phi )}&{\cos \theta \sin \phi \cos (\theta - \phi )}\\{\cos \theta \sin \phi \cos (\theta - \phi )}&{\sin \theta \sin \phi \cos (\theta - \phi )}\end{array}} \right]$
= $\cos (\theta - \phi )\,\left[ {\begin{array}{*{20}{c}}{\cos \theta \cos \phi }&{\cos \theta \sin \phi }\\{\cos \theta \sin \phi }&{\sin \theta \sin \phi }\end{array}} \right]$
= $O$, $\left( {\because \theta - \phi = \frac{\pi }{2}} \right)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 3 and 4 . determinant and metrices→STD 12 - 3 and 4 . determinant and metrices — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

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

Answer

Need a full question paper?

Explore more

Similar questions