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Summary

  • Let A be an n x n matrix. A is invertible if and only if
    • The columns of A span Rn
    • For every b in Rn, the system Ax=b is consistent
    • The rank of A is n
    • The columns of A are linear independent
    • The only solution to Ax=0 is the zero vector
    • The nullity of A is zero
    • The reduced row echelon form of A is In
    • A is a product of elementary matrices
    • There exists an n x n matrix B such that BA = In
    • There exists an n x n matrix C such that AC = In

onto

One-to-one

=

square matrix

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