How to prove that matrix A is invertible if and only if 0 is not the eigenvalue of a GOT IT

If a is invertible, then a must be a square matrix
From | λ e-A | = λ ^ n - (a11 + A22 +...) + ann)λ^(n-1) + … + (-1)^n|A|＝(λ-λ1)…… (λ - λ n), comparing the constant terms, we can get: | a | = the product of all eigenvalues
Therefore, the eigenvalues of | a | reversible a are not zero

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