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Mathematics
Problem
Let
A
=
(
k
1
−
2
3
)
A=\begin{pmatrix}k & 1 \\ -2 & 3\end{pmatrix}
A
=
(
k
−
2
1
3
)
and
B
=
(
3
−
1
2
k
)
B=\begin{pmatrix}3 & -1 \\ 2 & k\end{pmatrix}
B
=
(
3
2
−
1
k
)
. It is known that both
A
B
=
I
2
AB=I_2
A
B
=
I
2
and
B
A
=
I
2
BA=I_2
B
A
=
I
2
. Determine the value of
k
k
k
. a)
1
3
\dfrac13
3
1
b)
−
2
3
-\dfrac23
−
3
2
c)
−
1
3
-\dfrac13
−
3
1
d)
−
1
-1
−
1
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