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Problem
Problem
Let
A
=
[
3
−
5
7
−
12
]
A = \begin{bmatrix} 3 & -5 \\ 7 & -12 \end{bmatrix}
A
=
[
3
7
−
5
−
12
]
and
B
=
[
12
−
5
7
−
3
]
B = \begin{bmatrix} 12 & -5 \\ 7 & -3 \end{bmatrix}
B
=
[
12
7
−
5
−
3
]
be two given matrices, then
(
A
B
)
−
1
(AB)^{-1}
(
A
B
)
−
1
is : (a)
[
1
0
0
−
1
]
\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}
[
1
0
0
−
1
]
(b)
[
1
0
0
1
]
\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}
[
1
0
0
1
]
(c)
[
−
1
0
0
1
]
\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix}
[
−
1
0
0
1
]
(d)
[
0
1
1
0
]
\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}
[
0
1
1
0
]
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