@article {MATHEDUC.06141880,
author = {Chen, Lizhou},
title = {A generalization of the Cayley-Hamilton theorem.},
year = {2012},
journal = {American Mathematical Monthly},
volume = {119},
number = {4},
issn = {0002-9890},
pages = {340-342},
publisher = {Mathematical Association of America (MAA), Washington, DC},
doi = {10.4169/amer.math.monthly.119.04.340},
abstract = {The author proves that the determinant of the matrix $[b_{ij}A - a_{ij}B]_{n\times n}$, which is regarded as an $n\times n$ block matrix with pairwise commuting entries and where $A = [a_{ij}]_{n\times n}$, $B = [b_{ij}]_{n\times n }$ are two commuting square matrices of order $n$ over an arbitrary commutative ring, is exactly equal to the $n\times n$ zero matrix. If $B$ is the identity matrix, then the result is equivalent to the Cayley-Hamilton theorem.},
reviewer = {Costic\u{a} Moro\c sanu (Ia\c si)},
msc2010 = {H65xx},
identifier = {2013d.00583},
}