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Please solve RD Sharma Class 12 Chapter 5 Determinants Exercise Very Short Answer Question 21 maths textbook solution.

Answers (1)

Answer : \pm 1

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

Given: A \times A^{T}=I \quad \text { Find }|A|

Solution :

A A^{T}=I

\rightarrow Let's find determinate

\begin{aligned} &\left|A A^{T}\right|=|I| \\ &|A| \times\left|A^{T}\right|=|I| \end{aligned}

\rightarrow We know that |A|=\left|A^{T}\right| because both are transpose to each other

\begin{aligned} &|A| \times\left|A^{T}\right|=|I| \rightarrow \text { and }|I|=1 \\ &(|A|)^{2}=1 \\ &|A|=\sqrt{1} \\ &|A|=\pm 1 \end{aligned}

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