PROFESSOE CAYLEY ON THE THEOEY OF MATBICES. 



35 



or, what is the same thing, 



(XXX')+(D-A)(D'-A'){(XXX'))-' 

 is to a factor prhs equal to the matrix unity ; viz. writing 



the foregoing expression is 



=A( 1 . . . )• 



. 1 . . 



. . 1 . 



... 1 



The theorem is verified without difficulty by merely forming the expressions of the 

 compound matrices (X^^X') and (X'~'3(X"'). 



