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  • Need clarity, kindly explain! - Matrices and Determinants - JEE Main-5

What is order of idempotent matrix  A=\begin{bmatrix} 2 & 5&14 \\ 1 & 3& 8\\ -1&-2 &-6 \end{bmatrix}   

  • Option 1)

    2

  • Option 2)

    3

  • Option 3)

    4

  • Option 4)

    5

 

Answers (1)

best_answer

As we have learned

Idempotent matrix -

A^{2}=A

-

 

 A^2=\begin{bmatrix} 2 & 5 &14 \\ 1 & 3& 8\\ -1& -2&-6 \end{bmatrix}\begin{bmatrix} 2 &5 & 14\\ 1 & 3 & 8\\ -1 & -2 &-6 \end{bmatrix}=\begin{bmatrix} -5 &-3 & 16\\ -3& -2 &-10 \\ 2& 1&6 \end{bmatrix}

now if we multiply A^2 \times A^2 we get A^4=I.

Thus A is idempotent matrix of order = 4


Option 1)

2

Option 2)

3

Option 3)

4

Option 4)

5

Posted by

gaurav

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