SOLUTION: if A is a square matrix of order 3 such that |adjA|=36 then what is value of |A^T|

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Question 1042632: if A is a square matrix of order 3 such that |adjA|=36 then what is value of |A^T|
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
We have the fundamental relation
A%2Aadj%28A%29+=+abs%28A%29I%5B3%5D,
where abs%28A%29 is the determinant of A.
===> abs%28A%29%2A%28adj%28A%29%29+=+abs%28A%29%5E3,
since A is of order 3. (The determinant was applied on both sides.)
===>adj%28A%29+=++abs%28A%29%5E2,
===> abs%28A%29%5E2+=+36 ===> |A| = 6 or |A| = -6.
===> abs%28A%5ET%29+=+6 or abs%28A%5ET%29+=+-6, since abs%28A%29+=+abs%28A%5ET%29.