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  • Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 30 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 30 Maths Textbook Solution.

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Answer: AB-BAis skew symmetric matrix

Hint: We must know the basic of matrix multiplication

Given: Aand Bare symmetric matrix

Solution:

A^{T}=A          ……(i)

B^{T}=B          ……(ii)

Let AB-BA and take transpose

\left ( AB-BA \right )^{T}=\left ( AB \right )^{T}-\left ( BA \right )^{T}

                           =B^{T}A^{T}-A^{T}B^{T}

                           = BA-AB                   [From eqn(i) and (ii)]

AB-BA=-\left ( AB-BA \right )

So, AB-BAis skew symmetric matrix

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