28 PROFESSOR CATLET OX THE THEORY OF MATRICES. 



9. And similarly, 



n(T'-a')=( 



— 1 X «. «» 



-1 



) 



=( . • . -1 ) 

 ( . . -1 . ) 

 { . 1 - - } 

 ( 1 . . . ) 

 =(—d, —h, —I, —p ). 

 —c, —g, —k, —0 

 h, f, J^ n 



a, e, i, m 

 10, Hence also 



(T-a)(T+n)-' = (l+2m, 2n, 



2i , 1+2J, 



, m 



b, f, J, n 



c, g, k, 



d, h, I, p 

 (a, b, c, d), (e,f, g, h), {ij,k,l), {m,n,o,p) 



and 



2o, 



21 



-2e , -2/, \-2g, -2h 

 —2a, — 2J, -2c, l-2d 



(T+n)(T-n)-'=( 1-2(Z, -2h, -21, -2p ), 



-2c, l-2g, -2k, -2o 



2b, 2f, l+2y, 2n 



2a, 2e, 2i, l+2m 

 fio that these matrices are composed of terms which, except as to the signs, are the same 

 in each. 



11. Now in general if 



0=( a , ^ , y , 



«'5 /3', /, 



a" 5 /3", y", 



«'", /3"', y'", 

 then it is easy to see that 



n-0n=( y, y'", 

 S"5 y"5 



-I' , -y , 



— ^ , — y , 



S )5 



-/3", -a" 



/3', a' 



^ 5 « 



