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Mathematics
Problem
Let
P
P
P
and
Q
Q
Q
be
2
×
2
2\times 2
2
×
2
matrices such that
P
Q
=
I
2
PQ=I_2
P
Q
=
I
2
. Which one of the following statements is necessarily true? a)
Q
P
=
I
2
QP=I_2
QP
=
I
2
b)
P
Q
=
Q
P
PQ=QP
P
Q
=
QP
c)
det
(
P
)
=
det
(
Q
)
\det(P)=\det(Q)
det
(
P
)
=
det
(
Q
)
d)
P
+
Q
=
I
2
P+Q=I_2
P
+
Q
=
I
2
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