To test whether a 2×2 square matrix is invertible, first calculate its determinant. If the determinant is zero, the matrix has no inverse; if it is non-zero, the matrix is invertible. A square matrix is invertible exactly when its determinant is non-zero. The determinant is 2(4)-3(-5)=23, so it is invertible. So the decision depends entirely on whether the determinant equals zero or not.