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Mathematics
Problem
Let A and B be two invertible matrices of order
3
×
3
3 \times 3
3
×
3
. If
det
(
A
B
A
T
)
=
8
\det(ABA^T) = 8
det
(
A
B
A
T
)
=
8
and
det
(
A
B
−
1
)
=
8
\det(AB^{-1}) = 8
det
(
A
B
−
1
)
=
8
, then
det
(
B
A
−
1
B
T
)
\det(BA^{-1}B^T)
det
(
B
A
−
1
B
T
)
is equal to : [JEE-MAIN ONLINE-2019] (1) 16 (2)
1
16
\frac{1}{16}
16
1
(3)
1
4
\frac{1}{4}
4
1
(4) 1
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