# If A is a 33 matrix such that , then is equal to : Option 1) Option 2) Option 3) Option 4)

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)

This option is correct.

Option 2)

This option is incorrect.

Option 3)

This option is incorrect.

Option 4)

This option is incorrect.

N

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