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Explain Solution R. D. Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Multiple Choice Questions Question 39 maths Textbook Solution.

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Answer: Skew symmetric matrix

Given: If A and B are matrices of same order then AB^{T}-BA^{T}is

Hint: You must know about properties of transpose


Given that order of matrices A and B are same

Then we check it by taking transpose of AB^{T}-BA^{T}


\begin{array}{ll} \left(A B^{T}-B A^{T}\right)^{T}=\left(A B^{T}\right)^{T}-\left(B A^{T}\right)^{T} & {\left[(A-B)^{T}=A^{T}-B^{T}\right]} \\ =\left(B^{T}\right)^{T}(A)^{T}-\left(A^{T}\right)^{T} B^{T} & {\left[(A B)^{T}=B^{T} A^{T}\right]} \\ =B A^{T}-A B^{T} & {\left[\left(A^{T}\right)^{T}=A\right]} \\ =\left(A B^{T}-B A^{T}\right) \end{array}

AB^{T}-BA^{T} Is a skew symmetric matrix

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