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  • Please solve RD Sharma Class 12 Chapter 5 Determinants Exercise Very Short Answer Question 25 maths textbook solution.

Please solve RD Sharma Class 12 Chapter 5 Determinants Exercise Very Short Answer Question 25 maths textbook solution.

Answers (1)

Answer: 4

Hint: Here we use basic concept of determinant of matrix

Given:

\begin{aligned} &|A|=2 \\ &\text { Find }\left|A A^{T}\right| \end{aligned}

Solution :

\begin{aligned} &\left|A A^{T}\right|=|A| \times\left|A^{T}\right| \\ &\rightarrow \text { Here }\left|A^{T}\right|=|A| \end{aligned} because both are transpose to each other

So,

\begin{aligned} &\left|A A^{T}\right|=|A| \times\left|A^{T}\right| \\ &=|A| \times|A| \\ &=(|A|)^{2} \\ &=(2)^{2} \\ &\left|A A^{T}\right|=4 \end{aligned}

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