Chapter 2 - Matrices and Systems of Linear Equations - 2.6 The Inverse of a Square Matrix - Problems - Page 177: 8

$A^{-1}$ does not exist

Rank of a zero matrix is zero, we have: $rank(A) =0 \lt 2 = n$ According to the Theorem: Matrix A is invertible if and only $rank(A)=n$ Hence here, the matrix is not invertible, so it doesn't have the inverse.