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  • If A is a square matrix of order 3 such that then <img alt="|(adj A^{-1})^{-1}|" src="https://entrancec

If A is a square matrix of order 3 such that |A| = 2 then |(adj A^{-1})^{-1}| is

Option: 1

1


Option: 2

2


Option: 3

4


Option: 4

8


Answers (1)

best_answer

 

Inverse of a matrix -

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

-

 

 

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\: A^{-1} \right |=\left | A^{-1} \right |^{2}=\frac{1}{\left | A \right |^{2}}

\left |( adj\: A^{-1})^{-1} \right |=\frac{1}{\left | adj\: A^{-1} \right |}=\left | A \right |^{2}=2^{2}=4

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Gunjita

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