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  • If A is non singular matrix of order 3 , and |A| indicates the determinant of A , then |A^-1 (adj A) | is equal to .

If A is non singular matrix of order 3 , and |A| indicates the determinant of A , then |A^-1 (adj A) | is equal to .

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Solution:     We know that

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

    Moreover ,    AA^-1=I        ...........(2)

    From (2) , we have

                   left | A ight |left | A^-1 ight |=1     Rightarrow   left | A^-1 ight |=1/left | A ight |      ...........(3)

 Now,  left | A^-1(adjA) ight |=left | A^-1 ight |left | (adjA) ight |=left | A ight | 

Posted by

Deependra Verma

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