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