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Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 24 Maths Textbook Solution

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Answer: ABA^{T}is skew symmetric matrix

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

Given: B is skew symmetric matrix

ABA^{T}is skew symmetric or symmetric matrix


Bis Skew symmetric

So, B^{T}=-B

So, ABA^{T}

\rightarrowLet take transpose

=ABA^{T}=\left ( ABA^{T} \right )^{T}=AB^{T}A^{T}=A\left ( -B \right )A^{T}

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

\rightarrowSo, we clearly see that it satisfy the condition of skew symmetric

So, ABA^{T}is skew symmetric matrix

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