Question

If A and B are square matrices of order 3 such that |A| = − 1, |B| = 3, then find the value of |3 AB|.

Answer 1

\[\left| K A \right| = K^n \left| A \right| \left[\text{ n is the order of A }\right]\] 
\[ \Rightarrow \left| 3AB \right| = 3^3 \left| AB \right| . . . (1)\] 
\[\text{ If A and B are square matrices of the same order, then }\left| AB \right| = \left| A \right| \left| B \right| . So, \] 
\[\left| 3AB \right| = 3^3 \left| A \right| \left| B \right| \left[\text{ From eq . }(1) \right]\] 
\[ = 27 \times - 1 \times 3\] 
\[ = - 81\]