Question: 6. [6 marks] Let N be a 2 X 2 matrix such that N2 : 0. Prove that either N : 0 or N is

6. [6 marks] Let N be a 2 X 2 matrix such that N2 : 0. Prove that either N : 0 or N is similar to the matrix: 0 1 0 0 (Hint: View N as the matrix representation in the standard basis for an operator T : F2 > F2, so that T2 : 0, and then nd a basis 15' : {051,112} such that Teal : 0 and Tag : a1.)

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