Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Choose the correct answer in the following questions: If A equals [alpha beta gamma minus alpha] is such that A to power 2 equals I then (A) (B) (C) (D)

Choose the correct answer in the following questions:

    Q13.    If A = \begin{bmatrix} \alpha &\beta\\ \gamma &-\alpha \end{bmatrix} is such that A^2 = I

                (A)    1 + \alpha^2 + \beta \gamma = 0

                (B)    1 - \alpha^2 + \beta \gamma = 0

                (C)    1 - \alpha^2 - \beta \gamma = 0

                (D)    1 + \alpha^2 - \beta \gamma = 0

Answers (1)

best_answer

A = \begin{bmatrix} \alpha &\beta\\ \gamma &-\alpha \end{bmatrix}

A^2 = I

\begin{bmatrix} \alpha &\beta\\ \gamma &-\alpha \end{bmatrix}\begin{bmatrix} \alpha &\beta\\ \gamma &-\alpha \end{bmatrix}= \begin{bmatrix} 1 &0\\0&1 \end{bmatrix}

\begin{bmatrix} \alpha^{2} +\beta \gamma&\alpha \beta-\alpha \beta\\\alpha \gamma-\alpha \gamma&\beta \gamma+\alpha^{2} \end{bmatrix}= \begin{bmatrix} 1 &0\\0&1 \end{bmatrix}

\begin{bmatrix} \alpha^{2} +\beta \gamma&0\\0&\beta \gamma+\alpha^{2} \end{bmatrix}= \begin{bmatrix} 1 &0\\0&1 \end{bmatrix}

Thus we obtained that

\alpha^{2} +\beta \gamma=1

\Rightarrow 1-\alpha^{2} -\beta \gamma=0

Option C is correct.

 

 

 

 

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE practical exams 2026 will be cancelled over non-compliance with guidelines, says board

Latest Question