We are given that,

is a skew-symmetric matrix.

We need to find the value of x.

Let us understand what skew-symmetric matrix is.

A skew-symmetric matrix is a square matrix whose transpose equals its negative, that, it satisfies the condition

A skew symmetric matrix ⬄ A^T = -A

First, let us find –A.

Let us find the transpose of A.

We know that the transpose of a matrix is a new matrix whose rows are the columns of the original.

In matrix A,

1^st row of A = (0 1 -2)

2^nd row of A = (-1 0 3)

3^rd row of A = (x -3 0)

In the formation of matrix A^T,

1^st column of A^T = 1^st row of A = (0 1 -2)

2^nd column of A^T = 2^nd row of A = (-1 0 3)

3^rd column of A^T = 3^rd row of A = (x -3 0)

So,

Substituting the matrices –A and A^T, we get

-A = A^T

We know by the property of matrices,

This implies,

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

By comparing the corresponding elements of the two matrices,

x = 2

Thus, the value of x = 2.