- #1

- 101

- 25

$$

\lim_{t\to 0} (\chi_A(B) + \det(B)I)B^{-1} = 0

$$

where ##\chi_A## is the characteristic polynomial of ##A##. Note that ##\lim_{t\to 0} \chi_A(B) = \chi_A(A) = 0## by Cayley-Hamilton theorem.

This limit involves the product of a convergent to zero function and a divergent function. I'm not sure how to transform the limit in order to prove this.