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  • If A is order 3 non-singular matrix such that Det A=delta , then Det (adj A^-1) equals

If A is order 3 non-singular matrix such that Det A=delta , then Det (adj A^-1) equals

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Solution:         left | adjA ight |=left | A ight |^n-1  , where n=3

         Rightarrow              left | adjA ight |=left | A ight |^2

        Rightarrow            left | adjA^-1 ight |=left | A^-1 ight |^2      ............(1)

        Rightarrow     But        left | A^-1 ight |=1/left | A ight |=Delta ^-1

       Rightarrow            left | adjA^-1 ight |=(Delta ^-1)^2=Delta ^-2   

Posted by

Deependra Verma

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