Question

Let A and B be 4x4 matrices. Suppose that det(A) = 3 and det(B) = 5, find det(2A), det(A^-1B), det(A^3
) and det(A^T B)

Answer 1

use the following
\[\text{Det}(a\cdot A)=a^4\text{Det}(A)\]
\[\text{Det}(AB)=\text{Det}(A)\cdot \text{Det}(B)\]
\[\text{Det}(A^{-1})=\frac{1}{\text{Det}(A)}\]
\[\text{Det}(A^{T})=\text{Det}(A)\]

Answer 2

thanks, i didnt know the first or third property

Answer 3

in general if A in and nxn matrix then \[\text{Det}(a\cdot A)=a^n\text{Det}(A)\]

Answer 4

is*