Why is it that any square additive identity matrix (which is.?) must have the property that any product of it with another matrix of appropriate dimension is the additive identity?Why can the additive identity matrices not have multiplicative inverses?
The additive identity matrix is composed entirely of zeroes. Therefore its determinant is 0 and it is non-invertible. It is also an annihilator under multiplication, which is another reason it is non-invertible.
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The additive identity matrix contains all zero entries. Multiplying by this will always give you a matrix with zeros in all the entries.
