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Problems
Let
B
=
[
1
0
2
1
]
and
A
=
[
k
1
0
2
]
,
B=\begin{bmatrix}1 & 0\\2 & 1\end{bmatrix}\quad\text{and}\quad A=\begin{bmatrix}k & 1\\0 & 2\end{bmatrix},
B
=
[
1
2
0
1
]
and
A
=
[
k
0
1
2
]
,
…
Mathematics
Problem
Let
B
=
[
1
0
2
1
]
and
A
=
[
k
1
0
2
]
,
B=\begin{bmatrix}1 & 0\\2 & 1\end{bmatrix}\quad\text{and}\quad A=\begin{bmatrix}k & 1\\0 & 2\end{bmatrix},
B
=
[
1
2
0
1
]
and
A
=
[
k
0
1
2
]
,
where
k
k
k
is a real number. (i) Compute
A
B
AB
A
B
and
B
A
BA
B
A
in terms of
k
k
k
. (ii) Determine all real values of
k
k
k
for which
A
B
≠
B
A
AB\neq BA
A
B
=
B
A
. (iii) For the value(s) of
k
k
k
obtained in part (ii), find the matrix
A
B
−
B
A
AB-BA
A
B
−
B
A
.
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