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If A is a square matrix then, (A) A + AT is symmetric (B) AAT is skew - symmetric (C) AT + A is skew-symmetric(D) ATA is skew symmetric

If A is a square matrix then,
(A) A + AT is symmetric (B) AAT is skew - symmetric (C) AT + A is skew-symmetric(D) ATA is skew symmetric

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2 Answers

Arun
25758 Points
2 years ago
Dear student
 
let C = A + A^T
 
Now C^T = A^T + A 
 
hence C is a symmetric matrix.
 
So option A is correct.
 
Thanks and regards
Vikas TU
14149 Points
2 years ago
The determinant of a skew symmetric matrix of odd order is zero, which means skew symmetric matrix of an odd number are singular. Hence their inverse does not exist.

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