Question

If \(\rm A = \begin{bmatrix} 1 & 3 \\\ 4 & 2 \end{bmatrix} , \ \rm B = \begin{bmatrix} 2 & -1 \\\ 1 & 2 \end{bmatrix}\), then \(\rm |ABB'|=\)
1. 50
2. -250
3. 100
4. 250
5. None of these

Answer 1

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.