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  • Please Solve R D Sharma class 12 Chapter 4 Algbra of Matrices Exercise Multiple Choice Questions Question 1 Maths textbook Solution

Please Solve R.D.Sharma class 12 Chapter 4 Algbra of Matrices Exercise Multiple Choice Questions Question 1 Maths textbook Solution.

Answers (1)

Answer: The option (B) is correct. As the main diagonal elements are 1 except others which are 0, so it is a Unit Matrix.           

Given: A=\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1 \end{array}\right]

Solution:

\begin{aligned} A^{2} &=A \times A \\ &=\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1 \end{array}\right] \times\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1 \end{array}\right] \\ &=\left[\begin{array}{lll} 1+0+0 & 0+0+0 & 0+0+0 \\ 0+0+0 & 0+1+0 & 0+0+0 \\ a+0-a & 0+b-b & 0+0+1 \end{array}\right] \\ &=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right] \end{aligned}

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