Linear Algebra

A system of $n$ linear equations in $n$ variables $A X = B$ has a UNIQUE solution if and only if:

Options:

• (A) Rank of $A$ equals $n$ (i.e., $\det(A) \neq 0$)
• (B) Rank of $A$ is strictly less than $n$
• (C) Determinant of $A$ equals 0
• (D) Rank of augmented matrix $[A|B]$ is strictly greater than rank of $A$