I'm currently figuring out the following question but I 'm having trouble understanding it. The question is as follows:
Of the $4\times 4$ Matrix $A$ it's given that $\det (5A^3) = \det(A^T)$. Deduce the possible values of $\det(A)$."
I know the following:
A determinant of a transposed matrix should be the same as a determinant of the normal matrix.
Det $5*A^3$ should be $5^4*A$ with the $^4$ coming from the $4\times 4$ matrix, right?
That's the limit of my current knowledge though, anyone willing to explain what I'm missing to come to the correct equation?