Q:

Is the adjoint matrix $A^*$ defined?

Let $A=(a)$ be a $(1\times 1)$-matrix with entry  in an arbitrary commutative ring with identity, is the adjoint matrix $A^*$ defined?

A:

For a generic $1\times 1$ matrix over a commutative ring $R$, the adjugate (or adjoint) matrix is $I=(1)$, see wikipedia. Complex conjugation does not make sense in $R$, so the notation $A^*$ is not the best one.

