Check if a matrix is a Toeplitz matrix
Mathematica, 42 bytes

2Boole[#==ToeplitzMatrix[#&amp;@@@#,#&amp;@@#]]-1&amp;


Mathematica doesn't have a built-in to check whether something is a Toeplitz matrix, but it does have a built-in to generate one. So we generate one from the first column (#&amp;@@@#) and the first row (#&amp;@@#) of the input and check whether it's equal to the input. To convert the True/False result to 1/-1 we use Boole (to give 1 or 0) and then simply transform the result with 2x-1.