Correct Answer - Option 2 : -250
Concept:
Consider two matrices, A and B then
det(AB) = det(A)det(B)
Calculation:
\(\rm A=\begin{bmatrix} 1 & 3 \\\ 4 & 2 \end{bmatrix} \)
\(\\ det A=2-12\)
= -10
\(\rm B = \begin{bmatrix} 2 & -1 \\\ 1 & 2 \end{bmatrix} \)
\(\\detB=4-(-1)\)
= 5
\(\rm B'= \begin{bmatrix} 2 & 1 \\\ -1 & 2 \end{bmatrix} \)
\(\\detB=4-(-1)\)
= 5
\(\rm |ABB'|=|A||B||B^{'}|\)
= (-10)(5)(5)
= -250
Hence, option (2) is correct.