Let I denote the 3times3 identity matrix. Given any three distinct matrices A,B,Cin M3(R), which of the following statements is necessarily true?

(A) There exists Din M3(R) and a polynomial finR[X] satisfying f(A)=f(B)=f(C)=0 and f(D)=I.

Q30Section B (Part B)30 of 120

Polynomials in matrices — annihilating three matrices at once

Let $I$ denote the $3\times3$ identity matrix. Given any three distinct matrices $A,B,C\in M_3(\mathbb{R})$ , which of the following statements is necessarily true?

Pick an option to check your answer.

Keyboard: A–D answer · S solution · ←/→ previous/next