Find the value of $x$ given that the following two matrices have the same…

First, calculate the determinant of Matrix A by expanding along the first column:

$$\det(A) = 1 \cdot (x^2 - 1) = x^2 - 1$$

Next, calculate the determinant of Matrix B by expanding along the first row:

$$\det(B) = x(0 - x) - 1(x - 0) + 0 = -x^2 - x$$

Set the determinants equal to each other:

$$x^2 - 1 = -x^2 - x$$

Rearrange into a standard quadratic equation:

$$2x^2 + x - 1 = 0$$

Factor the quadratic equation:

$$(2x - 1)(x + 1) = 0$$

Solve for x:

$$x = 1/2 \quad \text{or} \quad x = -1$$