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From what I can tell from the definitions of a lower-triangular, upper-triangular, and diagonal matrices, I've come to the conclusion that the zero matrix is in the set of all of each type of matrix. Is this correct?

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Yes ${}{}{}{}{}{}$. –  copper.hat Feb 14 '13 at 20:09
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up vote 2 down vote accepted

A zero square matrix is lower triangular, upper triangular, and also diagonal.

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If an object meets the definition of three things then it is the three things. What are you confused about?

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The definition of those three things, for instance take the definition provided here: mathworld.wolfram.com/LowerTriangularMatrix.html I didn't find it particularly clear. The stumbling block was on could a_{ij} = 0. Apparently the answer is yes, yes it can. –  BrotherJack Feb 14 '13 at 20:19
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