I've been asked by my professor to identify a group of singular matrices. At first, I did not think this was possible, since a singular matrix is non-invertible by definition, yet to prove a groups existence, every such singular matrix must have an inverse. It has been brought to my attention, however, that a multiplicative identity need not be the typical diagonal "identity matrix" but can instead be any matrix for which AI=IA=A. For example, take the matrix [3 3] [0 0]. Since the determinant for this matrix is 0, it satisfies the singular aspect. However, my classmate is claiming that the multiplicative inverse for this matrix is [1/3 1/3] [0 0], which would indeed satisfy the above requirement of AI=IA=A. Is this possible? Please help, I'm so confused!!