Question

The inverse of a symmetric matrix is

• A. Symmetric
• B. Skew-symmetric
• C. Diagonal
• D. None of these

Answer 1

Answer: (A)

Symmetric

Let A be symmetric matrix.
$\Rightarrow A^{\prime }=A$
$\Rightarrow (A^{\prime }{)}^{-1}=(A{)}^{-1}$
$\Rightarrow (A^{-1}{)}^{\prime }=A^{-1}$
$\Rightarrow A^{-1}$ is symmetric.
Option $A$ is correct.