Solution
= Solution
The Pauli multiplication relations and $|\widehat n|=1$ give
$$
A^2=(\widehat n\cdot\boldsymbol\sigma)^2=I.
$$
Therefore the possible measurement outcomes, the <eigenvalues> of $A$, are
$$
\boxed{+1\quad\text{and}\quad-1}.
$$
= Solution
The Pauli multiplication relations and $|\widehat n|=1$ give
$$
A^2=(\widehat n\cdot\boldsymbol\sigma)^2=I.
$$
Therefore the possible measurement outcomes, the <eigenvalues> of $A$, are
$$
\boxed{+1\quad\text{and}\quad-1}.
$$