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

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