Science:Math Exam Resources/Courses/MATH152/April 2022/Question A13/Statement

Find ${\textstyle \det(X)}$, where ${\textstyle X}$ is a matrix that satisfies the equation ${\textstyle XA+B^{T}=C}$ and

$$A=\left[{\begin{array}{cc}2&4\\1&3\end{array}}\right],\ B=\left[{\begin{array}{cc}1&1\\-1&-2\end{array}}\right],\ C=\left[{\begin{array}{cc}3&2\\1&1\end{array}}\right].$$