question_answer

If A and B are matrices of order 3 and \[|A|\,\,=5,\] \[|B|\,\,=3,\] find \[|3AB|.\]

Answer:

Given, \[|A|\,\,=5,\] \[|B|\,\,=3\] We know that, \[|kA|\,\,={{k}^{n}}|A|,\] where A is matrix of order n. \[\therefore \] \[|3AB|\,\,={{3}^{3}}|A|\cdot |B|\]                         \[=27\times 5\times 3\]                         = 405