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Mathematics
Mathematics
Problem
Which of the following conditions is both necessary and sufficient for a
3
×
3
3\times 3
3
×
3
matrix
A
A
A
to possess an inverse? a)
rank
(
A
)
=
2
\operatorname{rank}(A)=2
rank
(
A
)
=
2
b)
det
(
A
)
≠
0
\det(A)\neq 0
det
(
A
)
=
0
c)
det
(
A
)
>
0
\det(A)>0
det
(
A
)
>
0
d)
trace
(
A
)
≠
0
\operatorname{trace}(A)\neq 0
trace
(
A
)
=
0
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