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  • Explain Solution R. D. Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Multiple Choice Questions Question 44 maths Textbook Solution.

Explain Solution R. D. Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Multiple Choice Questions Question 44 maths Textbook Solution.

Answers (1)

Answer: Skew symmetric

Given: A=\left[\begin{array}{ccc} 0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0 \end{array}\right]

Hint: matrix is skew symmetric if A^{T}=-A

Solution:

\begin{aligned} &A=\left[\begin{array}{ccc} 0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0 \end{array}\right] \\ &A^{T}=\left[\begin{array}{ccc} 0 & 5 & -8 \\ -5 & 0 & -12 \\ 8 & 12 & 0 \end{array}\right]=-\left[\begin{array}{ccc} 0 & -5 & 8 \\ 5 & 0 & -12 \\ -8 & -12 & 0 \end{array}\right]=-A \\ &\Rightarrow A^{T}=-A \end{aligned}

\therefore A is a skew symmetric matrix

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