Question

How is determinant of inverse related to determinant of mtrix?

Answer 1

it holds that det ( A B ) = det ( A ) det ( B ) , so that det ( A ) det ( A - 1 ) = 1 . in other words an invertible matrix has (multiplicatively) invertible determinant... on the other hand if the determinant is invertible, then so is the matrix itself because of the relation no its adjugate .




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