# Let a be a root of the equation x 2 + x + 1 = 0 and the matrix A = 1 3 2 2 4 11 1 1 1 é ù ê ú ê ú a a ê ú ë û a a , then the matrix A 31 is equal to:

Question:

Let $\alpha$ be a root of the equation $x^{2}+x+1=0$

and the matrix $A=\frac{1}{\sqrt{3}}\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & \alpha & \alpha^{2} \\ 1 & \alpha^{2} & \alpha^{4}\end{array}\right]$, then the matrix $A^{31}$

is equal to:

1. $A$

2. $I_{3}$

3. $A^{2}$

4. $A^{3}$

Correct Option: 4

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year Jan. 7, 2020 (I)

Solution:

### Related Questions

• If $\alpha=\cos ^{-1}\left(\frac{3}{5}\right), \beta=\tan ^{-1}\left(\frac{1}{3}\right)$, where $0<\alpha, \beta<\frac{\pi}{2}$, then $\alpha-\beta$ is equal to:

View Solution

• A value of $x$ satisfying the equation $\sin \left[\cot ^{-1}(1+x)\right]=\cos$ $\left[\tan ^{-1} x\right]$, is :

View Solution

• The principal value of $\tan ^{-1}\left(\cot \frac{43 \pi}{4}\right)$ is:

View Solution

• The number of solutions of the equation, $\sin ^{-1} x=2 \tan ^{-1} x$ (in principal values) is :

View Solution

• A value of $\tan ^{-1}\left(\sin \left(\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\right)\right.$ is

View Solution

• A value of $\tan ^{-1}\left(\sin \left(\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\right)\right.$ is

View Solution

• The largest interval lying in $\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$ for which the function, $f(x)=4^{-x^{2}}+\cos ^{-1}\left(\frac{x}{2}-1\right)+\log (\cos x)$, is defined, is

View Solution

• The domain of the function $f(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^{2}}}$ is

View Solution

• The trigonometric equation $\sin ^{-1} x=2 \sin ^{-1} a$ has a solution for

View Solution

• $$\cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x$$ then $\sin x=$

View Solution

error: Content is protected !!
Download App