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  • Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 27 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 27 Maths Textbook Solution.

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Answer: \left ( A^{n} \right )^{T}=A^{n}

Hint: We must know the basic of symmetric

Given: Ais symmetric

Solution: A=A^{T} as Ais symmetric

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

So, \left ( A^{n} \right )^{T}=A^{n}

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