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Mathematics
Mathematics
Problem
Let
A
,
B
A,\,B
A
,
B
and
C
C
C
be matrices of suitable orders so that the indicated operations are defined. Which one of the following statements is always true? a)
(
B
+
C
)
A
=
B
A
+
A
C
(B + C)A = BA + AC
(
B
+
C
)
A
=
B
A
+
A
C
b)
A
(
B
+
C
)
=
A
B
+
A
C
A(B + C) = AB + AC
A
(
B
+
C
)
=
A
B
+
A
C
c)
A
B
=
B
A
AB = BA
A
B
=
B
A
d)
(
A
B
)
C
=
A
C
B
(AB)C = AC\,B
(
A
B
)
C
=
A
C
B
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