Mathematics Tripos Papers

  • Part IA
  • Part IB
  • Part II
  • FAQ

3.I.1A

Algebra and Geometry | Part IA, 2002

Given two real non-zero 2×22 \times 22×2 matrices AAA and BBB, with AB=0A B=0AB=0, show that AAA maps R2\mathbb{R}^{2}R2 onto a line. Is it always true that BA=0?B A=0 ?BA=0? Show that there is always a non-zero matrix CCC with CA=0=ACC A=0=A CCA=0=AC. Justify your answers.

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