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Mathematics
Mathematics
Problem
1. Matrices
A
A
A
and
B
B
B
will be inverse of each other only if (A)
A
B
=
B
A
(
B
)
A
B
=
B
A
=
0
\mathrm{AB}=\mathrm{BA}(\mathrm{B}) \mathrm{AB}=\mathrm{BA}=0
AB
=
BA
(
B
)
AB
=
BA
=
0
(C)
A
B
=
0
,
B
A
=
I
(
D
)
A
B
=
B
A
=
I
\mathrm{AB}=0, \mathrm{BA}=\mathrm{I}(\mathrm{D}) \mathrm{AB}=\mathrm{BA}=\mathrm{I}
AB
=
0
,
BA
=
I
(
D
)
AB
=
BA
=
I
(A)
m
a
t
h
r
m
A
B
=
m
a
t
h
r
m
B
A
mathrm{AB}= mathrm{BA}
ma
t
h
r
m
A
B
=
ma
t
h
r
m
B
A
(B)
m
a
t
h
r
m
A
B
=
m
a
t
h
r
m
B
A
=
0
mathrm{AB}= mathrm{BA}=0
ma
t
h
r
m
A
B
=
ma
t
h
r
m
B
A
=
0
(C)
m
a
t
h
r
m
A
B
=
0
,
m
a
t
h
r
m
B
A
=
m
a
t
h
r
m
I
mathrm{AB}=0, mathrm{BA}= mathrm{I}
ma
t
h
r
m
A
B
=
0
,
ma
t
h
r
m
B
A
=
ma
t
h
r
m
I
(D)
m
a
t
h
r
m
A
B
=
m
a
t
h
r
m
B
A
=
m
a
t
h
r
m
I
mathrm{AB}= mathrm{BA}= mathrm{I}
ma
t
h
r
m
A
B
=
ma
t
h
r
m
B
A
=
ma
t
h
r
m
I
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