Suppose a 3×3 matrix B(k) satisfies det(B(k))=k2+1. Which statement about the invertibility of B(k) for real k is true?
a) B(k) is singular only when k=0.
b) B(k) is non-singular for all real k.
c) B(k) is non-singular only for k>0.
d) B(k) is singular when k=±1.