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Question Number 112505 by bemath last updated on 08/Sep/20

$$\mathrm{Given}\mathrm{matrix}\mathrm{A}=\left(\begin{array}{c}10\\ 23\end{array}\right),\mathrm{B}=\left(\begin{array}{c}-1-3\\ 20\end{array}\right)$$$$\mathrm{and}\mathrm{AX}+2\mathrm{B}=\mathrm{I}.\mathrm{what}\mathrm{the}\mathrm{value}$$$$\mathrm{of}\det \left(\mathrm{X}\right)?$$

Answered by john santu last updated on 08/Sep/20

$$\iff AX=\left(\begin{array}{c}10\\ 01\end{array}\right)-\left(\begin{array}{c}-2-6\\ 40\end{array}\right)$$$$\iff AX=\left(\begin{array}{c}36\\ -41\end{array}\right).$$$$det\left(X\right)=\frac{\left|\begin{array}{c}36\\ -41\end{array}\right|}{\left|\begin{array}{c}10\\ 23\end{array}\right|}=\frac{27}{3}=9.$$

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