SOLUTION: A &B are square matrices of order 3 s.t | A |=-1,|B|=3.then the determinant |3AB|=-81 prove it

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Question 960889: A &B are square matrices of order 3 s.t | A |=-1,|B|=3.then the determinant |3AB|=-81 prove it
Answer by rothauserc(4718) About Me  (Show Source):
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|3AB|=-81 prove it
note that |AB| = |A| |B| and |kA| = k^n |A| where n is rank of matrix, therefore
|3AB| = (3^3) |A| |B| = 27 * -1 * 3 = -81