We are given that,

We need to find the value of (x, y).

Multiply the matrices on the right hand side of the equation,

For z₁₁: Dot multiply the 1^st row of first matrix and 1^st column of second matrix, then sum up.

(2 1)(1 -2) = 2 × 1 + 1 × -2

⇒ (2 1)(1 -2) = 2 – 2

⇒ (2 1)(1 -2) = 0

So,

For z₂₁: Dot multiply the 2^nd row of first matrix and 1^st column of second matrix, then sum up.

(4 3)(1 -2) = 4 × 1 + 3 × (-2)

⇒ (4 3)(1 -2) = 4 – 6

⇒ (4 3)(1 -2) = -2

So,

Equate the resulting matrix to the given matrix equation.

We know by the property of matrices,

This implies,

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

Therefore,

x + y = 0

x – y = -2

Adding these two equations, we get

(x + y) + (x – y) = 0 + (-2)

⇒ x + y + x – y = -2

⇒ x + x + y – y = -2

⇒ 2x + 0 = -2

⇒ 2x = -2

⇒ x = -1

Putting x = -1 in

x + y = 0

⇒ (-1) + y = 0

⇒ -1 + y = 0

⇒ y = 1

So, putting values of x and y from above in (x, y), we get

(x, y) = (-1, 1)

Thus, (x, y) is (-1, 1).