If A, B are square matrices of same order and B is skew-symmetric matrix, then show that A'BA is skew -symmetric.

Explanation

To show that \( A^T B A \) is a skew-symmetric matrix given that \( B \) is a skew-symmetric matrix, we will follow these steps:

### Step 1: Understand the definition of a skew-symmetric matrix
A matrix \( B \) is skew-symmetric if \( B^T = -B \).

### Step 2: Take the transpose of \( A^T B A \)
We need to find the transpose of the matrix \( A^T B A \). Using the property of transposes, we have:
\[
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