Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

Let A be a matrix such that A\cdot \begin{bmatrix} 1 &2 \\ 0 & 3 \end{bmatrix}  a scalar matrix and \left | 3A \right |=108. Then A2 equals : 

  • Option 1)

    \begin{bmatrix} 4 &-32 \\ 0 & 36 \end{bmatrix}

     

     

     

  • Option 2)

    \begin{bmatrix} 36 &0 \\ -32 & 4 \end{bmatrix}

  • Option 3)

    \begin{bmatrix} 4 &0 \\ -32 & 36 \end{bmatrix}

  • Option 4)

    \begin{bmatrix} 36 &-32 \\ 0& 4 \end{bmatrix}

 

Answers (2)

best_answer

As we learned 

 

Scalar Matrix -

A diagonal matrix whose all the elements are equal is called a scalar matrix 

- wherein

 

 

A\cdot \begin{bmatrix} 1 &2 \\ 0& 3 \end{bmatrix}    is a scalar matrix 

\left | 3A \right |=108

Let scalar matrix be \begin{bmatrix} k & 0\\ 0 &k \end{bmatrix}

A\begin{bmatrix} 1 &2 \\ 0&3 \end{bmatrix}=\begin{bmatrix} k & 0\\ 0 &k \end{bmatrix}

A=\begin{bmatrix} k & 0\\ 0 &k \end{bmatrix}\begin{bmatrix} 1 &2 \\ 0&3 \end{bmatrix}^{-1}

A=\begin{bmatrix} k & 0\\ 0 &k \end{bmatrix}\begin{bmatrix} 1 &\frac{-2}{3} \\ 0&\frac{1}{3} \end{bmatrix}

A=\begin{bmatrix} k &- \frac{2}{3}k\\ 0 &\frac{k}{3} \end{bmatrix}   also \left | 3A \right |=108   

\Rightarrow 3k^{2}=108\Rightarrow k=\pm 6

Take k = 6 

A^{2}=\begin{bmatrix} 36 & -32\\ 0 & 4 \end{bmatrix}

 


Option 1)

\begin{bmatrix} 4 &-32 \\ 0 & 36 \end{bmatrix}

 

 

 

Option 2)

\begin{bmatrix} 36 &0 \\ -32 & 4 \end{bmatrix}

Option 3)

\begin{bmatrix} 4 &0 \\ -32 & 36 \end{bmatrix}

Option 4)

\begin{bmatrix} 36 &-32 \\ 0& 4 \end{bmatrix}

Posted by

Himanshu

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main Result 2024 Live: JEE Mains session 2 results at jeemain.nta.ac.in soon; rank predictor
anam-khan

JEE Main 2024 session 2 final answer key out at jeemain.nta.ac.in; steps to check probable scores
anam-khan

JEE Main Result 2024 Live: Download session 2 final answer key at jeemain.nta.ac.in; rank predictor, cutoff

Latest Question