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Mathematics
Mathematics
Problem
Let
A
=
[
0
1
0
0
]
A = \begin{bmatrix}0 & 1 \\ 0 & 0\end{bmatrix}
A
=
[
0
0
1
0
]
and
B
=
[
0
0
1
0
]
B = \begin{bmatrix}0 & 0 \\ 1 & 0\end{bmatrix}
B
=
[
0
1
0
0
]
. Which of the following statements is true? a)
A
B
=
B
A
=
O
AB = BA = O
A
B
=
B
A
=
O
b)
A
B
≠
B
A
AB \neq BA
A
B
=
B
A
and both
A
B
AB
A
B
and
B
A
BA
B
A
are
non-zero
\text{non-zero}
non-zero
c)
A
B
=
B
A
≠
O
AB = BA \neq O
A
B
=
B
A
=
O
d)
A
B
≠
O
but
B
A
=
O
AB \neq O \text{ but } BA = O
A
B
=
O
but
B
A
=
O
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