What is defined as a matrix of all zeros except for the main diagonal consisting of all 1s?

The correct answer, the identity matrix, is characterized by having all elements equal to zero, except for the diagonal elements, which are all equal to one. This structure signifies that the identity matrix serves as the multiplicative identity in matrix arithmetic, meaning that when it multiplies another matrix, it leaves that matrix unchanged. For instance, if you have any square matrix A, multiplying it by the identity matrix will result in A itself (i.e., A * I = A). This property is fundamental in linear algebra, particularly when solving systems of equations or performing transformations.

It's worth noting that while "unit matrix" can also refer to this type of matrix in some contexts, it is not the most universally accepted term in linear algebra compared to "identity matrix." The zero matrix, in contrast, consists entirely of zeros and does not possess any non-zero diagonal elements. A diagonal matrix can contain non-zero values on its diagonal, but it may include values other than just ones, and these values would not necessarily be confined to only the identity matrix properties.