Class 12 Matrices · Assertion Reason1 Marksassertion_reason

Class 12 Maths · Matrices · Assertion Reason #28

Assertion: For every pair of same-order real symmetric matrices A,B, the matrix AB−BA is symmetric. Reason: A real square matrix M is skew-symmetric exactly when M=−Mᵀ.

(A) Both A and R are true, and R correctly explains A.
(B) Both A and R are true, but R does not correctly explain A.
(C) A is true, but R is false.
(D) A is false, but R is true.

✅ Step-by-Step Solution

Final Answer: Option (D): A is false, but R is true.

(AB−BA)ᵀ=BA−AB=−(AB−BA), so it is skew-symmetric. It need not be zero: A=diag(1,2), B=[[0,1],[1,0]] give a nonzero skew-symmetric commutator, which is not symmetric. Thus A is false and R true.

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Class 12 Maths · Matrices · Assertion Reason #28

✅ Step-by-Step Solution

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