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How many of the following matrices have an eigenvalue 1? [ [1 0],[0 0] ], [ [0 1],[0 0] ], [ [1 -1],[1 1] ] and [ [-1 0],[1 -1] ]

1. one
2. two
3. three
4. four

Correct answer: one

Solution

Eigenvalues: [[1,0],[0,0]] -> 1,0 (has 1); [[0,1],[0,0]] -> 0,0 (no); [[1,-1],[1,1]] -> 1+/-i (no); [[-1,0],[1,-1]] -> -1,-1 (no). Only one matrix has eigenvalue 1.

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