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

$$\begin{gathered} \left|AB\right|=\left|A\right|\times \left|B\right| \\ \left|A\right|=3,AB=I \\ \Rightarrow \left|AB\right|=1 \\ \Rightarrow \left|A\right|\times \left|B\right|=1 \\ 3\times \left|B\right|=1 \\ \left|B\right|=\frac{1}{3} \end{gathered}$$