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 = 2x(x + 1) – (x + 3)(2(x + 1))

⇒ LHS = (2x² + 2x) – (x + 3)(2x + 2)

⇒ LHS = (2x² + 2x) – (2x² + 2x + 6x + 6)

⇒ LHS = (2x² + 2x) – (2x² + 8x + 6)

⇒ LHS = 2x² + 2x – 2x² – 8x – 6

⇒ LHS = 2x² – 2x² + 2x – 8x – 6

⇒ LHS = -6x – 6

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

⇒ RHS = 1 × 3 – 5 × 3

⇒ RHS = 3 – 15

⇒ RHS = -12

Now,

LHS = RHS

⇒ -6x – 6 = -12

⇒ -6x = -12 + 6

⇒ -6x = -6

⇒ x = 1

Thus, the value of x is 1.