question_answer

The total number of matrices for which \[{{A}^{T}}A=3{{I}_{3}}\] is :-                                                                         [JEE Main 9-4-2019 Afternoon]

A) 6                     

B)   2

C) 3                                 

D) 4

Correct Answer: D

Solution :

\[{{A}^{T}}A=3{{I}_{3}}\] \[8{{x}^{2}}=3\] \[6{{y}^{2}}=3\] \[{{x}^{2}}=3/8\] \[{{y}^{2}}=1/2\] \[x=\pm \sqrt{\frac{3}{8}};y=\pm \sqrt{\frac{1}{2}}\]