If A and B are symmetric matrices then (

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

If A and B are symmetric matrices then (AB+ BA) is :

Options:

Symmetric matrix

Skew-symmetric matrix

Diagonal matrix

Scalar matrix

Correct Answer:

Symmetric matrix

Explanation:

given A = A^T

B = B^T

so (AB + BA)^T = (AB)^T + (BA)^T

(as (A + B)^T = A^T + B^T))

⇒ B^TA^T + A^TB^T

(as (PQ)^T = Q^TP^T)

⇒ BA + AB

so (AB + BA)^T = (AB + BA)

symmetric matrix