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If A and B are symmetric matrices of the same order, then
  • a)
    AB is symmetric matrix
  • b)
    AB – BA is a symmetric matrix
  • c)
    A – B is a skew-symmetric matrix
  • d)
    AB + BA is a symmetric matrix
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If A and B are symmetric matrices of the same order, thena)AB is symme...
If A and B are symmetric matrices of the same order, then , AB + BA is always a symmetric matrix.
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If A and B are symmetric matrices of the same order, thena)AB is symme...
Properties of Symmetric Matrices
Symmetric matrices have the property that they are equal to their own transpose, i.e., A = A^T. Given two symmetric matrices A and B of the same order:

Explanation:

AB + BA
- When we multiply two symmetric matrices AB and BA, we get AB + BA.
- Since A and B are symmetric matrices, A^T = A and B^T = B.
- (AB)^T = B^T A^T = BA (transpose of product is product of transposes)
- Therefore, AB + BA is equal to itself, making it symmetric.
Therefore, the correct option is:

d) AB + BA is a symmetric matrix
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If A and B are symmetric matrices of the same order, thena)AB is symmetric matrixb)AB – BA is a symmetric matrixc)A – B is a skew-symmetric matrixd)AB + BA is a symmetric matrixCorrect answer is option 'D'. Can you explain this answer?
Question Description
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