iran-konkur 2023 Q33

iran-konkur · Other · konkur-riazi_1402_general Matrices Determinant and Rank Computation
33. If $A = \begin{bmatrix} \log_5^2 & \log_5^2 \\ \log_5^2 & \log_5^2 \end{bmatrix}$ and $B = \begin{bmatrix} 6|A| & 2|A| \\ 3|A| & 36|A| \end{bmatrix}$, what is the determinant of $B$?
  • [(1)] $\dfrac{9}{4}$
  • [(2)] $\dfrac{15}{4}$
  • [(3)] $\dfrac{9}{8}$
  • [(4)] $\dfrac{15}{8}$
\textbf{33.} If $A = \begin{bmatrix} \log_5^2 & \log_5^2 \\ \log_5^2 & \log_5^2 \end{bmatrix}$ and $B = \begin{bmatrix} 6|A| & 2|A| \\ 3|A| & 36|A| \end{bmatrix}$, what is the determinant of $B$?

\begin{itemize}
    \item[(1)] $\dfrac{9}{4}$
    \item[(2)] $\dfrac{15}{4}$
    \item[(3)] $\dfrac{9}{8}$
    \item[(4)] $\dfrac{15}{8}$
\end{itemize}