Determinants of Matrices det(4A) equals?

Question

Suppose A is a 4 x 4 matrix such that $\det(A) = 1/64$. What will $\det(4A^{-1})^T$ be equal to?

Here's my thinking,
$\det(A^T) = \det(A)$
I has no effect on the determinant. And $\det(A^{-1}) = 1/\det(A)$
so $\det(4A^{-1}) = \det(4\times64)$ = can't be 256?

I don't understand, Please help me! THANKS!

Answer 1

If $A$ is a square $n$ matrix, $\mathrm{det}(x.A)=x^n.\mathrm{det}(A)$.

So here, $\mathrm{det}(4A^{-1})=4^4 . \mathrm{det}(A^{-1})=256. \mathrm{det}(A)^{-1}=256*64$