If A is a square matrix, then A + A^T is - Vidyadip

MCQ

If $ A$ is a square matrix, then $A + {A^T}$ is

A
Non singular matrix
✓
Symmetric matrix
C
Skew-symmetric matrix
D
Unit matrix

✓

Answer

Correct option: B.

Symmetric matrix

b
(b) $A + {A^T}$ is a square matrix.

${(A + {A^T})^T} = {A^T} + {({A^T})^T} = {A^T} + A$

Hence $A$ is a symmetric matrix.

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