We are given that,

We need to find the value of x.

Determinant of 2 × 2 matrix is found as,

Let us take left hand side (LHS) of the given matrix equation.

⇒ LHS = (x + 1)(x + 2) – (x – 1)(x – 3)

⇒ LHS = (x² + x + 2x + 2) – (x² – x – 3x + 3)

⇒ LHS = (x² + 3x + 2) – (x² – 4x + 3)

⇒ LHS = x² + 3x + 2 – x² + 4x – 3

⇒ LHS = x² – x² + 3x + 4x + 2 – 3

⇒ LHS = 7x – 1

Let us take right hand side (RHS) of the given matrix equation.

⇒ RHS = 4 × 3 – (-1) × 1

⇒ RHS = 12 + 1

⇒ RHS = 13

Now,

LHS = RHS

⇒ 7x – 1 = 13

⇒ 7x = 13 + 1

⇒ 7x = 14

⇒ x = 2

Thus, the value of x is 2.