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For an invertible matrix
MATHEMATICS · Single correct · CBSE · Mathematics · Matrices · Matrices
Problem
For an invertible matrix
A
A
A
, which one of the following statements is ALWAYS true? (a)
(
A
−
1
)
−
1
=
A
T
(A^{-1})^{-1}=A^{T}
(
A
−
1
)
−
1
=
A
T
(b)
A
−
1
+
I
=
(
A
+
I
)
−
1
A^{-1}+I=(A+I)^{-1}
A
−
1
+
I
=
(
A
+
I
)
−
1
(c)
(
A
−
1
)
T
=
(
A
T
)
−
1
(A^{-1})^{T}=(A^{T})^{-1}
(
A
−
1
)
T
=
(
A
T
)
−
1
(d)
(
A
T
)
−
1
=
A
(A^{T})^{-1}=A
(
A
T
)
−
1
=
A
Related theory
Transpose of a Matrix
Matrices
Matrix Operations
Adjoint and inverse
Properties of matrix operations
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