SOLUTION: If the determinant of the adjoint of matrix X of order 3 = 25. Find the determinant of the inverse of matrix X?

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Question 1184163: If the determinant of the adjoint of matrix X of order 3 = 25. Find the determinant of the inverse of matrix X?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

For any matrix A, where n is the order of the matrix

%28det%28A%29%5E%22%22%29%5E%28n-1%29%22%22=%22%22det%28adj%28A%29%5E%22%22%29

Substitute A=X and n=3 = (the order of X)

%28det%28X%29%5E%22%22%29%5E%283-1%29%22%22=%22%22det%28adj%28X%29%5E%22%22%29

%28det%28X%29%5E%22%22%29%5E2%22%22=%22%2225

%28det%28X%29%5E%22%22%29%5E2%22%22=%22%2225

det%28X%29%22%22=%22%22%22%22+%2B-+5

The determinant of the inverse of a given invertible matrix is
the reciprocal of the determinant of the given invertible matrix.

det%28X%5E%28-1%29%29%22%22=%22%22%22%22+%2B-+1%2F5

Edwin