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  • Need Solution for R.D. Sharma Maths Class 12 Chapter 4 Algebra of Matrices Exercise Multiple choice Questions Question 23 Maths Textbook Solution.

Need Solution for R.D. Sharma Maths Class 12 Chapter 4 Algebra of Matrices Exercise Multiple choice Questions Question 23 Maths Textbook Solution.

Answers (1)

Answer: The correct option is (D), none of these.

Given: \mathrm{A}=\left[a_{i j}\right] is a Square matrix of even order such that a_{i j}=i^{2}-j^{2}

Solution:

From   a_{i j}=i^{2}-j^{2}

\begin{gathered} \Rightarrow a_{11}=12-12=0 \\ a_{12}=12-22=-10 \\ a_{21}=22-12=10 \\ a_{22}=22-22=0 \end{gathered}

\begin{aligned} &\therefore A=\left[\begin{array}{cc} 0 & -10 \\ 10 & 0 \end{array}\right] \\ &A^{T}=\left[\begin{array}{cc} 0 & 10 \\ -10 & 0 \end{array}\right] \\ &-A=\left[\begin{array}{cc} 0 & 10 \\ -10 & 0 \end{array}\right] \end{aligned}

So,A^{T}=-A

\begin{aligned} |A| &=0(0)-(-10) 10 \\ &=0+100 \\ &=100 \neq 0 \end{aligned}

So, the correct option is (D).

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