Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Matrices

Question:

If A is non-identity invertible symmetric matrix, then $A^{-1}$ is :

Options:

Symmetric matrix

Skew-symmetric matrix

Identity matrix

Zero matrix

Correct Answer:

Symmetric matrix

Explanation:

The correct answer is Option (1) → Symmetric matrix

A is invertible

$⇒ AA^T=I$

so $A^{-1}=A^T$

A is symmetric

$⇒A^{-1}$ is symmetric