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Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 19 Maths Textbook Solution.

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Answer: Ais skew symmetric matrix

Hint: Here we should know the basics of matrix, skew and symmetric matrix

Given: A is square matrix and a_{ij}=i^{2}-j^{2}

Solution: Let A is square 2\times2 matrix

So, A=\begin{bmatrix} 1^{2}-1^{2} &1^{2}-2^{2} \\ 2^{2}-1^{2}& 2^{2} -2^{2}\end{bmatrix}

A=\begin{bmatrix} 0 &-3 \\ 3 & 0 \end{bmatrix}

So, Let A^{T}

A^{T}=\begin{bmatrix} 0 &3 \\ -3& 0 \end{bmatrix}

So, Here A^{T}=-A

So, Ais skew symmetric

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