I'm working on the Eq.9.77 in Peskin (page 304):
To demonstrate this, we need only apply standard identities from linear algebra. First notice that, if a matrix $B$ has eigenvalues $b_i ,$ we can write its determinant as $$ \det{B} ~=~ \prod_{i}{b_i} ~~= \exp{\left[ \sum_{i}{\log{b_i}} \right]} ~=~ \exp{\left[ \operatorname{Tr}{\left(\log{B}\right)} \right]} \,, \tag{9.77} $$ where the logarithm of a matrix is defined by its power series.
However, I test the identity and find it doesn't work.
For $B=\{\{3, -2, 4\}, \{-2, 6, 2\}, \{4, 2, 3\}\} ,$ the left-hand side of the Eq.(9.77) is -98, and the right is 54.
Why does this happen? What are the conditions for this identity to be true? How to prove it?