If `A`
is a non-singular
symmetric matrix, write whether `A^(-1)`
is symmetric or skew-symmetric.
Text Solution
AI Generated Solution
To determine whether \( A^{-1} \) is symmetric or skew-symmetric when \( A \) is a non-singular symmetric matrix, we can follow these steps:
### Step 1: Understand the definitions
- A matrix \( A \) is **symmetric** if \( A^T = A \).
- A matrix \( A \) is **skew-symmetric** if \( A^T = -A \).
- A matrix is **non-singular** if its determinant is non-zero, meaning it has an inverse.
### Step 2: Use the property of the transpose of the inverse
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