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I am reading a book that contains the following text.

A square matrix P is said to be a permutation matrix if each row and each column of P contains a single element 1, and the remaining elements are zero.

My questions are:

  1. why is "contains" used? why not "contain"? Since there is a "and" before "contains".
  2. why not "zeros" for the last word in the sentence?
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  1. This is a particular case of compound subject, one or more nouns joined with a conjunction. When compound subjects are preceded by "each", "every", and certain other words, they are rendered singular, in an exception to the general rules. This explains the singular verb agreement in your example.

    So: "the cup and bowl contain milk", but "each cup and each bowl contains milk".

    Your Dictionary
    University of West Florida
    Cuny School of Law
    Southeastern Louisiana University

  2. Here, "zero" is used as an adjective, rather than as a plural noun. From Merriam-Webster:

    a : of, relating to, or being a zero
    b : having no magnitude or quantity : not any zero growth zero tolerance

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