Question

The inverse of a symmetric matrix is ______.

Options

• symmetric

• skew-symmetric

• diagonal matrix

• singular matrix

Answer 1

The inverse of a symmetric matrix is symmetric.

Explanation:

If A is a symmetric matrix, then

A = A^T

⇒ A^–1 = (A^T)^–1

⇒ A^–1 = (A^–1)^T

⇒ A^–1 is a symmetric matrix.