Chapter 11 - Systems of Equations and Inequalities - 11.3 Systems of Linear Equations: Determinants - 11.3 Assess Your Understanding - Page 743: 52

$x=-1$ or $x=1$

We know that for a matrix \[ \left[\begin{array}{rr} a & b \\ c &d \\ \end{array} \right] \] the determinant, $D=ad-bc.$ Hence, here we have \begin{align*} D&=(x\cdot x)-(1\cdot3)\\ D&=x^2-3\\ -2&=x^2-3\\ -2+3&=x^2\\ 1&=x^2\\ \pm\sqrt{1}&=\sqrt{x^2}\\ \pm1&=x\end{align*}