If we have C=($A^t$)$^2$BA$^3$B$^-$$^1$A$^-$$^3$ and detA=-2 and detB doesnt equal 0, how do we calculate det C?
I know that the transpose of a matrix does not affect the determinant. Does this mean that ($A^t$)$^2$=(-2)$^2$=4?
And then how is A$^-$$^3$ affected? Does this mean the inverse of A cubed? And how does the inverse affect the determinant? Thanks