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  • Please solve RD Sharma class 12 chapter 5 Determinants exercise Fill in the blanks question 37 maths textbook solution

Please solve RD Sharma class 12 chapter 5 Determinants exercise Fill in the blanks question 37 maths textbook solution

Answers (1)

Answer: -4

Hint: Here, we use basic component of determinant

Given: A is square matrix of order 3

            So, n = 3

            \left | A \right |=2

Solution:

            Here, \left |-A A^{T} \right |

            So, \left | -A \right |\times \left |A^{T} \right |

            Here, \left |A^{T} \right |=\left | A \right | because both are transpose to each other

            So, \left | -A \right |\times \left | A \right |

            Let’s take -1 common

            \begin{aligned} &-1([A]) \times|A| \\ &-1(2) \times 2[|A|=2] \\ &S o,\left|-A A^{T}\right|=-4 \end{aligned}

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