If A is a 3\times3 matrix such that \left | 5. adjA \right |=5, then \left | A \right | is equal to :

  • Option 1)

    \pm \: \frac{1}{5}

  • Option 2)

    \pm \: 5

  • Option 3)

    \pm \: 1

  • Option 4)

    \pm \: \frac{1}{25}

 

Answers (2)

As we learnt in 

Property of adjoint of A -

\left | adj A \right |=\left | A \right |^{n-1}  

- wherein

adj A denotes adjoint of A and  \left |A \right |  denotes determinant  of A and n is the order of the matrix

 

 \left | adj\left ( A \right ) \right |=\left | A \right |^{n-1}

\left | K\:adj\left ( A \right ) \right |=K^{n}\left | adj\left ( A \right ) \right |

So that, put n = 3

\therefore \left | 5\:adj\left ( A \right ) \right |= 125\left | adj\left ( A \right ) \right |

\therefore 125\left | adj\left ( A \right ) \right |=5

\therefore \left | adj\left ( A \right ) \right |= \frac{1}{25}

But \left | adj\left ( A \right ) \right |= \left | A \right |^{2}

\therefore \left | A \right |^{2}= \frac{1}{25}

\left | A \right |= \pm \frac{1}{5}


Option 1)

\pm \: \frac{1}{5}

This option is correct.

Option 2)

\pm \: 5

This option is incorrect.

Option 3)

\pm \: 1

This option is incorrect.

Option 4)

\pm \: \frac{1}{25}

This option is incorrect.

N neha

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