Which of the following conditions holds true for a skew-symmetric matrix?

The correct option is A=IA.

To understand why this condition holds true for a skew-symmetric matrix, let us review the definition of a skew-symmetric matrix and the properties of matrix multiplication involving the identity matrix.

A matrix satisfies skew-symmetry if it is a square matrix whose transpose is equal to its negative.

Let the matrix be:
$A$
Its skew-symmetric property is defined as:
$A=-A^{\prime }$
where the transpose of the matrix is denoted by:
$A^{\prime }$

Next, let us consider the identity matrix:
$I$
The identity matrix of order
$n$
serves as the multiplicative identity for any square matrix of the same order. This means that multiplying any square matrix by the identity matrix does not alter its values.

This fundamental property of matrix multiplication is written as:
$A=IA=AI$
Since a skew-symmetric matrix is, by definition, a square matrix, this general property holds true for it as well.

Therefore, the relation:
$A=IA$
holds true for a skew-symmetric matrix.