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  • Give answer! For a 3 x 3 matrix A, if det A = 4, then det (Adj A) equals

For a 3 x 3 matrix A, if det A = 4, then det (Adj A) equals

  • Option 1)

    -4

  • Option 2)

    4

  • Option 3)

    16

  • Option 4)

    64

 

Answers (1)

best_answer

As we have learned

Property of adjoint of A -

adj\left ( adjA \right )=\left | A \right |^{n-2}A

- wherein

adjA  is adjoint of A , \left | A \right | is determinant of A and n is order of A

 

 

Since A Adj A = | A | I

                                                = \begin{bmatrix} \left | A \right | & 0 &0 \\ 0& \left | A \right | &0 \\ 0 &0 & \left | A \right | \end{bmatrix}

                        \therefore det (A Adj A)

                                                = \begin{bmatrix} \left | A \right | & 0 &0 \\ 0& \left | A \right | &0 \\ 0 &0 & \left | A \right | \end{bmatrix}=\left | A \right |^{3}

                        \therefore |A| |Adj A| = |A|3

                        \therefore |Adj A| = |A|2 = (4)2 = 16


Option 1)

-4

Option 2)

4

Option 3)

16

Option 4)

64

Posted by

gaurav

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