357] 
A SUPPLEMENTARY MEMOIR ON THE THEORY OF MATRICES. 
441 
8. We have 
n (r + n') = ( 
1 
)( a, b, c, d 
1 
e, f, 9, h 
-1 
i , j, k, l 
-1 
m, n, o, p 
{a, e, i, to), (b, f, j, n), (c, g, k, o), (d, h, l, p) 
= ( • 
1 ) 
>> 
99 
99 99 
( • 
1 
• 
) 
99 
99 99 
( • 
- 1 
) 
99 
99 
99 99 
(-1 
• 
• 
• 
) 
99 
99 
99 99 
= ( 
m, 
n, 
o, 
P 
)• 
i > 
k, 
l 
-e , 
~9> 
-h 
— a, 
-b, 
— c, 
-d 
9. And similarly, 
n (T' -n') = ( 
. 
- 1 
)( 
a, e, 
i, TO 
) . 
- 1 
• 
b, /, 
j> n 
■ 
1 
. 
• 
c, g, 
k, o 
1 
• 
d, h, 
l, p 
(a, b, c, 
d), (e, f, g, 
h), (i, j, k, l), (to, n, o, p) 
«( 
. 
. 
-1 
) 
99 
99 
99 99 
( . 
. 
-1 
) 
99 
99 
•99 99 
( . 
1 
• 
) 
99 
99 
99 99 
( 
1 
• 
• 
• 
) 
99 
99 
99 99 
= ( 
— d, 
-h, 
-l, 
-p 
). 
-c, 
~9> 
-k, 
— 0 
b, 
f, 
j > 
n 
a, 
e, 
i, 
TO 
10. Hence also 
(T — fl) (T + ß)- 1 = ( 
1 + 2 to, 
2 n, 
2 o, 
2 P ) 
2 i , 
1 + 2'j, 
2k, 
21 
-2e , 
-2/, 
1-2 g, 
— 2h 
— 2 a , 
-2b, 
-2c, 1 
-2d 
C. V. 
56