Let \({\rm{A}} = \left[ {\begin{array}{*{20}{c}} {\rm x + y}& \rm y\\ {\rm 2x}&{\rm x - y} \end{array}} \right],\;\rm B = \left[ {\begin{array}{*{20}{c}} 2\\ { - 1} \end{array}} \right]\) and \(\rm C = \left[ {\begin{array}{*{20}{c}} 3\\ 2 \end{array}} \right]\). If AB = C, then what is the value of the determinant of the matrix A?

Let \({\rm{A}} = \left[ {\begin{array}{*{20}{c}} {\rm x + y}& \rm y\\

1.	Let \({\rm{A}} = \left[ {\begin{array}{{20}{c}} {\rm x + y}& \rm y\\ {\rm 2x}&{\rm x - y} \end{array}} \right],\;\rm B = \left[ {\begin{array}{{20}{c}} 2\\ { - 1} \end{array}} \right]\) and \(\rm C = \left[ {\begin{array}{*{20}{c}} 3\\ 2 \end{array}} \right]\). If AB = C, then what is the value of the determinant of the matrix A?
A.	-10
B.	-14
C.	-24
D.	-34
Answer» C. -24