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Please solve RD Sharma solution for Maths Class 12 Chapter 5 Determinants Exercise Very short question Question 15 for maths textbook solution.

Answers (1)

Answer:1

Hint: Here we use basic concept of identity matrix and determinant of matrix

Given: I_{3} denotes the 3 \times 3 identify matrix

Solution :

3 \times 3 identity matrix is I_{3}

So,

I_{3}=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]

\rightarrow Lets find determinate

\begin{aligned} &|I|=\left|\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right| \\ &=1\left|\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right|-0\left|\begin{array}{ll} 0 & 0 \\ 0 & 1 \end{array}\right|+0\left|\begin{array}{ll} 0 & 1 \\ 0 & 0 \end{array}\right| \\ &=1(1-0)-0(0-0)+0(0-0) \\ &=1(1)=1 \\ &|A|=1 \end{aligned}

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