Question

If A and B are square matrices of order 3 and that |A| = –2, |B| = 4, then |2AB| = __________.

Answer 1

Given:
A and B are square matrices of order 3
|A| = –2
|B| = 4


$$\begin{gathered} \mathrm{Now}, \\ \left|2AB\right|=\left|2A\right|\left|B\right|\left(\because \left|AB\right|=\left|A\right|\left|B\right|,\mathrm{if}\mathrm{they}\mathrm{are}\mathrm{square}\mathrm{matrices}\mathrm{of}\mathrm{same}\mathrm{order}\right) \\ =\left|2A\right|\times 4\left(\because \left|B\right|=4\right) \\ =2^3\left|A\right|\times 4\left(\because \mathrm{Order}\mathrm{of}A\mathrm{is}3\times 3\right) \\ =32\left|A\right| \\ =32\times \left(-2\right)\left(\because \left|A\right|=-2\right) \\ =-64 \end{gathered}$$

Hence, |2AB| = –64.