The reason the matrix A has to be square for det(A-XI_n) is a) because we cannot subtract a matrix A from another matrix B if their dimensions aren’t the same a

The reason the matrix A has to be square for det(A-XI_n) is a) because we cannot subtract a matrix A from another matrix B if their dimensions aren’t the same and since XI_n is a nxn matrix A has to be an nxn matrix as well and b) because the determinant is only defined for square matrices.