We are given with

We need to find the value of k.

Take Left Hand Side (LHS) of the matrix equation.

In multiplication of matrices,

For c₁₁: dot multiply the matching members of 1^st row of first matrix and 1^st column of second matrix and then sum up.

(a₁₁ a₁₂)(b₁₁ b₂₁) = a₁₁ × b₁₁ + a₁₂ × b₂₁

Thus,

(1 2)(3 2) = 1 × 3 + 2 × 2

⇒ (1 2)(3 2) = 3 + 4

⇒ (1 2)(3 2) = 7

For c₁₂: dot multiply the matching members of 1^st row of first matrix and 2^nd column of second matrix and then sum up.

(a₁₁ a₁₂)(b₁₂ b₂₂) = a �₁₁ × b₁₂ + a₁₂ × b₂₂

Thus,

(1 2)(1 5) = 1 × 1 + 2 × 5

⇒ (1 2)(1 5) = 1 + 10

⇒ (1 2)(1 5) = 11

Similarly, do the same for other elements.

Since,

Substituting the value of LHS,

We know by the property of matrices,

This implies,

a₁₁ = b₁₁, a₁₂ = b₁₂, a₂₁ = b₂₁ and a₂₂ = b₂₂

Thus,

7 = 7

11 = 11

17 = k

23 = 23

Hence, k = 17.