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Suppose $A$ is a $3\times3$ matrix with entries $(a_{ij})$ and that $A=LU$ is an LU factorization of $A$ without partial pivots.

If the top-left entry of $L$ is zero, what is true of $A$?

$A$ is invertible

$A$ is upper triangular

$A$ is lower triangular

All first row entries of $A$ equal $0$

All first column entries of $A$ equal $0$