Q74 / 180 · KCET 2019 · Mathematics
If \( A=\left[\begin{array}{ll}1 & 3 \\ 4 & 2\end{array}\right], B=\left[\begin{array}{cc}2 & -1 \\ 1 & 2\end{array}\right] \) then \( \left|A B B^{\prime}\right|= \)
- Correct answerA\( -250 \)
- B\( 250 \)
- C\( 50 \)
- D\( 100 \)
Solution
(A)
\[ \begin{array}{l} A=\left[\begin{array}{ll} 1 & 3 \\ 4 & 2 \end{array}\right], B=\left[\begin{array}{cc} 2 & -1 \\ 1 & 2 \end{array}\right] \\ B^{\prime}=\left[\begin{array}{cc} 2 & 1 \\ -1 & 2 \end{array}\right] \\ \left|A B B^{\prime}\right|=|A||B|\left|B^{\prime}\right| \\ =(2-12) \times(4+1) \times(4+1) \\ =-10 \times 5 \times 5=-250 \end{array} \]
\[ \begin{array}{l} A=\left[\begin{array}{ll} 1 & 3 \\ 4 & 2 \end{array}\right], B=\left[\begin{array}{cc} 2 & -1 \\ 1 & 2 \end{array}\right] \\ B^{\prime}=\left[\begin{array}{cc} 2 & 1 \\ -1 & 2 \end{array}\right] \\ \left|A B B^{\prime}\right|=|A||B|\left|B^{\prime}\right| \\ =(2-12) \times(4+1) \times(4+1) \\ =-10 \times 5 \times 5=-250 \end{array} \]
Hence, the correct answer is option: 'A'.