Here is the matrix, which I'm asked to give the determinant of. How do I read this?
$$R^{(1)}:= \begin{bmatrix} 1 \\ & \ddots \\ & & 0 & \cdots & 1 & &\\ & & \vdots & \ddots & \vdots \\ & & 1 & \cdots & 0\\ & & & & & \ddots \\ & & & & & & 1 \end{bmatrix}$$
How do I deal with the dots and find the determinant?
As FraGrechi said, we can transform this matrix into the identity matrix, whose determinant is $1$; however, since we swap two rows, we need to multiply this by $-1$, giving us our final determinate of $-1$.