In this chapter we present an efficient iterative method of order six for the inclusion of the inverse of a given regular matrix. To provide the upper error bound of the outer matrix for the inverse matrix, we combine point and interval iterations. The new method is relied on a suitable matrix identity and a modification of a hyper-power method. This method is also feasible in the case of a full-rank \(m\times n\) matrix, producing the interval sequence which converges to the Moore–Penrose inverse. It is shown that computational efficiency of the proposed method is equal or higher than the methods of hyper-power’s type. Theoretical results are confirmed by numerical experiments.