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Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 31 Maths Textbook Solution.

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Answer: \begin{bmatrix} 0 &0 &0 &0 \end{bmatrix} or Null matrix

Hint: we should use the basic concept of symmetric as well as skew symmetric matrix,

For example,

A^{T}=A       (Ais symmetric matrix)

A^{T}=-A         (Ais skew symmetric matrix)

Given: Write a square matrix which is both symmetric as well as skew symmetric

Solution: Let’s take basic properties of symmetric and skew symmetric

\begin{gathered} \quad A^{T}=A \\ -A^{T}=-A \\ \hline A^{T}-A^{T}=A-(-A) \\ 0=2 A \\ A=0 \end{gathered}

So, a skew symmetric or symmetric matrix can be a square matrix’s.

Example is,

O_{2\times2}=\begin{bmatrix} 0 &0 \\ 0 & 0 \end{bmatrix}

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