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

MCQ

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

A
Unit matrix
B
Symmetric matrix
✓
Skew symmetric matrix
D
Zero matrix

✓

Answer

Correct option: C.

Skew symmetric matrix

c
(c) ${(A - {A^T})^T} = {A^T} - {({A^T})^T}$

= ${A^T} - A$

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

So, $A - {A^T}$ is a skew symmetric matrix.

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