Question

If A is a square matrix such that |A| = 2, write the value of |A A^T|.

Answer 1

$$\begin{gathered} \mathrm{In}\mathrm{a}\mathrm{square}\mathrm{matrix},\left|\mathrm{A}\right|=\left|{\mathrm{A}}^{\mathrm{T}}\right|. \\ \mathrm{Since}\mathrm{they}\mathrm{are}\mathrm{of}\mathrm{same}\mathrm{order},\left|\mathrm{A}{\mathrm{A}}^{\mathrm{T}}\right|=\left|\mathrm{A}\right|\left|{\mathrm{A}}^{\mathrm{T}}\right|. \\ \mathrm{Given}:\left|\mathrm{A}\right|=2 \\ \Rightarrow \left|\mathrm{A}{\mathrm{A}}^{\mathrm{T}}\right|=2\times 2=4 \end{gathered}$$