- #1
rachbomb
- 4
- 0
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!
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!