If A is a square matrix of order n × n such that |A| = λ, then write the value of |-A|.

Question

Philoid · Accepted Answer

Since |kA|= k^m|A|

Given that k=-1, m=n and |A|=λ, we get

|-A|=(-1)ⁿ×λ

Hence, |-A|=λ if n is even and |-A|=-λ if n is odd.