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  • Give answer! Let A be any 3×3 invertible matrix. Then which one of the following is not always true ?

 Let A be any 3×3 invertible matrix.  Then which one of the following is not always true ?

  • Option 1)

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

  • Option 2)

    adj\left ( adj\left ( A \right ) \right )=\left | A \right |.A

  • Option 3)

    adj\left ( adj\left ( A \right ) \right )=\left | A \right |^{2}.\left ( adj\left ( A \right ) \right )^{-1}

  • Option 4)

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

 

Answers (2)

best_answer

As we learnt in 

Inverse of a matrix -

 A^{-1}=\frac{1}{\left | A \right |}\cdot adjA

-

 

 Option 1: A^{-1} =\frac{adj(A)}{\left | A \right |}\, \, (By\ formula)

 

Option 2: adj (adj (A)) == | A| ^{n-2}A

Put n = 3

\therefore adj (adj (A))= | A| ^{3-2}A = \left | A \right |A

Option 3: adj (adj (A))= | A| ^{n-1} (adj (A))^{-1}

Put n = 3


Option 1)

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

This option is incorrect.

Option 2)

adj\left ( adj\left ( A \right ) \right )=\left | A \right |.A

This option is incorrect.

Option 3)

adj\left ( adj\left ( A \right ) \right )=\left | A \right |^{2}.\left ( adj\left ( A \right ) \right )^{-1}

This option is incorrect.

Option 4)

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

This option is correct.

Posted by

prateek

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