#### Provide solution for RD Sharma maths Class 12 Chapter 5 Determinants Exercise VSQ Question 29 maths textbook solution.

Answer : $(-1)^{n} \lambda$

Hint : Here we use basic concept of determinant of matrix

Given :

A is $\text {n}\times \text {n}$ order of matrix, $|A|=\lambda$

$\rightarrow$ Then find value of $\left | -A \right |$

Solution :

Here we know that

$|k A|=k^{n}|A|$

where n is order of matrix

k is constant

So, $\text {k = -1}\; \; \; \; \; \; \; ....(1)$

\begin{aligned} &\rightarrow|k A|=k^{n}|A| \\ &|-1 A|=(-1)^{n}|A| \; \; \; \quad \text { .from } \operatorname{eqn}(1) \\ &|-1 A|=(-1)^{n} \lambda \end{aligned}