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Mathematics
Mathematics
Problem
For a non-singular
3
×
3
3\times 3
3
×
3
matrix
A
A
A
, which one of the following relations is always true? a)
adj
(
A
)
=
1
det
(
A
)
A
−
1
\operatorname{adj}(A)=\dfrac{1}{\det(A)}\,A^{-1}
adj
(
A
)
=
det
(
A
)
1
A
−
1
b)
adj
(
A
)
=
det
(
A
)
A
−
1
\operatorname{adj}(A)=\det(A)\,A^{-1}
adj
(
A
)
=
det
(
A
)
A
−
1
c)
adj
(
A
)
=
det
(
A
)
A
T
\operatorname{adj}(A)=\det(A)\,A^{T}
adj
(
A
)
=
det
(
A
)
A
T
d)
adj
(
A
)
=
A
det
(
A
)
\operatorname{adj}(A)=\dfrac{A}{\det(A)}
adj
(
A
)
=
det
(
A
)
A
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