Question

If A and B are square matrices of order 3 and |A| = 5, |B| = 5, then |3AB| = ____________.

Answer 1

Given:
A and B are square matrices of order 3
|A| = 5
|B| = 5


$$\begin{gathered} \mathrm{Now}, \\ \left|3AB\right|=\left|3A\right|\left|B\right|\left(\because \left|AB\right|=\left|A\right|\left|B\right|,\mathrm{if}\mathrm{they}\mathrm{are}\mathrm{square}\mathrm{matrices}\mathrm{of}\mathrm{same}\mathrm{order}\right) \\ =\left|3A\right|\times 5\left(\because \left|B\right|=5\right) \\ =3^3\left|A\right|\times 5\left(\because \mathrm{Order}\mathrm{of}A\mathrm{is}3\times 3\right) \\ =135\left|A\right| \\ =135\times \left(5\right)\left(\because \left|A\right|=5\right) \\ =675 \end{gathered}$$

Hence, |3AB| = 675.