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Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 23 Maths Textbook Solution

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Answer: AB=BA

Both must be commutative to each other

Hint: Here to solve this we use the basic concept of skew symmetric matrix

Given: A \: and \: B is symmetric matrix


A \: and \: B is symmetric then

A=A^{T}\cdot \cdot \cdot \cdot \cdot \left ( i \right )

B=B^{T}\cdot \cdot \cdot \cdot \cdot \left ( ii \right )

→So, let AB can be symmetricAB=\left ( AB^{T} \right ) =B^{T}A^{T} =BA          

From equation (i) and (ii)AB=BA

→So, condition is A \: and \: B matrix must be commutative and AB=BA

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