Question

If A and B are square matrices of the same order such that |A| = 3 and AB = I, then write the value of |B|.

Answer 1

Since A & B are square matrices of the same order, by the property of determinants we get
\[\left| AB \right| = \left| A \right| \times \left| B \right|\] 
\[\left| A \right| = 3, AB = I \] 
\[ \Rightarrow \left| AB \right| = 1\] 
\[ \Rightarrow \left| A \right| \times \left| B \right| = 1\] 
\[3 \times \left| B \right| = 1\] 
\[\left| B \right| = \frac{1}{3}\]