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For invertible matrices and of the same order
MATHEMATICS · Single correct · CBSE · Mathematics · Matrices · Matrices
Problem
For invertible matrices
A
A
A
and
B
B
B
of the same order, evaluate
(
(
A
−
1
B
)
T
)
−
1
((A^{-1}B)^{T})^{-1}
((
A
−
1
B
)
T
)
−
1
. (a)
(
B
T
)
−
1
A
T
(B^{T})^{-1}A^{T}
(
B
T
)
−
1
A
T
(b)
A
T
(
B
T
)
−
1
A^{T}(B^{T})^{-1}
A
T
(
B
T
)
−
1
(c)
B
T
(
A
T
)
−
1
B^{T}(A^{T})^{-1}
B
T
(
A
T
)
−
1
(d)
(
A
T
)
−
1
B
T
(A^{T})^{-1}B^{T}
(
A
T
)
−
1
B
T
Related theory
Transpose of a Matrix
Matrices
Determinants
Adjoint and inverse
Properties of transpose
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