Concept:The determinant of a 3×3 matrix is expanded along a row or column to obtain an equation in x.Explanation:Given: ​x01​10x​314​​=0.Expand along the first row:x⋅(0⋅4−1⋅x)−1⋅(0⋅4−1⋅1)+3⋅(0⋅x−0⋅1)=0.Simplify each term:First term: x⋅(0−x)=−x2.Second term: −1⋅(0−1)=1.Third term: 3⋅(0−0)=0.So the equation becomes: −x2+1=0.Rearrange: x2=1.Take square roots: x=±1.Thus, x=−1 or x=1.Answer:x=−1 or x=1, i.e., option C.