Question

If $A=\left[\begin{array}{cc}\sin \theta & \tan \theta \\ \tan \theta & \sin \theta \end{array}\right]$ has no multiplicative inverse, then

• A. $\theta =0^o$
  
• B. $\theta ={45}^o$
  
• C. $\theta ={60}^o$
• D. $\theta ={30}^o$
  

Answer 1

The correct option is A $\theta =0^o$

Since, A has no multiplicative inverse, $|A|=0$

Therefore,

$si{n}^2\theta -ta{n}^2\theta =0$

$si{n}^2\theta =ta{n}^2\theta$

$\sin \theta =\tan \theta$

$\theta =0^o$