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

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}