Answer:
a) det(A)=96; b) det(A)=m;
Step-by-step explanation:
If we have a [tex]n \times n[/tex] matrix A and a constant [tex]t \in \mathbb{R}[/tex]. It holds that [tex]\det(tA)=t^n\det(A)[/tex], hence
(a) If A is a [tex]5x5[/tex] matrix and [tex]\det(A)=3[/tex], then we have
[tex]\det(2A)=2^5\cdot \det(A)= 32 \cdot 3=96[/tex]
(b) If A is [tex]100 \times 100[/tex] matrix and [tex]\det(A)=m[/tex], then we have
[tex]\det(-A)=(-1)^{100}\det(A)=(-1)^{100}\cdot m=1 \cdot m = m[/tex]
