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If A be any matrix then AAT and ATA are
  • a)
    Skew Symmetric
  • b)
    Both are Symmetric
  • c)
    Hermitian
  • d)
    Skew Hermitian
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If A be any matrix then AAT and ATA area)Skew Symmetricb)Both are Symm...
Let A be real matrix , then take
(AAT)T = (AT)AT = AAT
⇒ AAT is Symmetric
now
(ATA)T = AT(AT)T = AT
⇒ ATA is Symmetric
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Most Upvoted Answer
If A be any matrix then AAT and ATA area)Skew Symmetricb)Both are Symm...
Explanation:

To determine the properties of the matrices AAT and ATA, we need to understand the definitions of these matrices and the properties they possess.

Definition of AAT:
The matrix AAT is obtained by multiplying matrix A with its transpose. The resulting matrix has the same number of rows as A and the same number of columns as the transpose of A.

Definition of ATA:
The matrix ATA is obtained by multiplying the transpose of matrix A with A. The resulting matrix has the same number of rows as the transpose of A and the same number of columns as A.

Properties of AAT:
When we multiply A by its transpose, the resulting matrix AAT will always be a symmetric matrix. This is because the entry (i, j) in AAT is the dot product of the ith row of A with the jth row of A, which is the same as the dot product of the jth row of A with the ith row of A. Therefore, AAT is symmetric.

Properties of ATA:
Similarly, when we multiply the transpose of A with A, the resulting matrix ATA will also be a symmetric matrix. This is because the entry (i, j) in ATA is the dot product of the ith column of A with the jth column of A, which is the same as the dot product of the jth column of A with the ith column of A. Therefore, ATA is symmetric.

Conclusion:
From the properties stated above, we can conclude that both AAT and ATA are symmetric matrices. Therefore, the correct answer is option 'B' - Both are symmetric.
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If A be any matrix then AAT and ATA area)Skew Symmetricb)Both are Symmetricc)Hermitiand)Skew HermitianCorrect answer is option 'B'. Can you explain this answer?
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