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

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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}

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