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Find an example for square matrices A and B of the same size such that: det(A + B) ≠ det(A) + det(B)?

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Find an example for square matrices A and B of the same size such that: det(A + B) ≠ det(A) + det(B)?

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  1. A:

    [1 0]

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    B:

    [0 0]

    [0 1]

    det(A) = 1*0 - 0*0 = 0

    det(B) = 0*1 - 0*0 = 0

    det (A + B) = 1, because A+B=I or

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    [0 1]

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