Problem 1
: [10 points] In each part of this problem,
A
,
B
, and
are square matrices.
C
(a)
Show that
.
1
1
(
)
AB
B
A
−
−
=
1
−
(b)
Use the results from part (a) to write down
1
(
)
ABC
−
in terms of
1
A
−
,
1
B
−
, and
1
C
−
.
(c)
True or false: If
A
λ
is an eigenvalue of
A
, then
3
A
λ
is an eigenvalue of
. State your
reasoning.
3
A
1

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