in Linear Algebra
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If the determinant of an $n \times n$ matrix $A$ is zero then

  1. rank of $A$ is $n$
  2. rank of $A\leq n-2$
  3. $A$ has at least one zero eigen value
  4. the system of equations $Ax=0$ has no solution other than trivial solution


 

in Linear Algebra
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Best answer
Product of Eigen values = Determinant
Determinant is 0 i.e. one of the Eigen Value is 0
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for a singular matrix product of eigen value is zero

product of eigen value is equal det of matrix and sum is equal to trace
Answer:

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