Question

what is solution of |A+B|

Answer 1

i know if |A|\[|A| \neq 0\]
\[|A+B|=|(I+B A^{-1})A|=|I+B A^{-1}|*|A|\]

Answer 2

if we get \[C=BA ^{-1}\] we have
\[|I+C||A|\]
.
if possible i like some expand of it, for example write expand by Eigenvalues |I+C| or ...