question_answer

If A is an invertible matrix of order \[3\times 3\] such that | A| = 5, find the value of \[|{{A}^{-1}}|.\]

Answer:

We have, \[|A|\,\,=5\] We know that, \[|{{A}^{-\,1}}|\,\,=\,\,|A{{|}^{-\,1}}={{(5)}^{-\,1}}=\frac{1}{5}\]