SOLUTION: If A is a non singular matrices of order 3 and |A|=-3 find |adj. A|

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Question 1021823: If A is a non singular matrices of order 3 and |A|=-3 find |adj. A|
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28adjA%29+=+abs%28A%29%5E%28n-1%29 by a property of the adjoint operator.
==> abs%28adjA%29+=+abs%28A%29%5E%28n-1%29+=+abs%28A%29%5E2+=+%28-3%29%5E2+=+9, where n = 3.
Proof.
For an invertible nxn matrix, A%2A%28adjA%29+=+abs%28A%29I%5Bn%5D%29
==> abs%28A%29abs%28adjA%29+=+%28abs%28A%29%29%5En,
the last equation arising from the determinant of a scalar matrix and the identity matrix.
==> abs%28adjA%29+=+%28abs%28A%29%29%5E%28n-1%29, since abs%28A%29+%3C%3E0