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Mathematics
Problem
Let
A
−
1
=
(
1
−
1
0
1
)
A^{-1}=\begin{pmatrix}1 & -1\\ 0 & 1\end{pmatrix}
A
−
1
=
(
1
0
−
1
1
)
and
B
−
1
=
(
2
0
1
1
)
B^{-1}=\begin{pmatrix}2 & 0\\ 1 & 1\end{pmatrix}
B
−
1
=
(
2
1
0
1
)
for two invertible
2
×
2
2\times2
2
×
2
matrices
A
A
A
and
B
B
B
. Find
(
B
A
T
)
−
1
(BA^{T})^{-1}
(
B
A
T
)
−
1
. a)
(
2
0
−
1
2
)
\begin{pmatrix}2 & 0\\ -1 & 2\end{pmatrix}
(
2
−
1
0
2
)
b)
(
2
0
−
1
1
)
\begin{pmatrix}2 & 0\\ -1 & 1\end{pmatrix}
(
2
−
1
0
1
)
c)
(
2
0
0
1
)
\begin{pmatrix}2 & 0\\ 0 & 1\end{pmatrix}
(
2
0
0
1
)
d)
(
2
−
2
1
0
)
\begin{pmatrix}2 & -2\\ 1 & 0\end{pmatrix}
(
2
1
−
2
0
)
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