We show that for two 2×2 integral matrices A, B, if the product AB\nis nil-clean then BA may not be nil-clean. Despite the fact that for many\nspecial cases, BA is also nil-clean, we finally found three counterexamples.\nAll the way, the computer aid was decisive.

Solid waste is all-inclusive, encompassing the heterogeneous mass of throw away from the urban community as well as the more homogeneous accumulation of agricultural, industrial and mineral wastes. The general objective of the study was to assess solid waste disposal practices and its management in Lalibella city. The data was collected through questionnaire, interview and survey. 86 sample households were selected using systematic random sampling technique and the data collected was analyzed by using descriptive statistical procedures presented using frequency, percentage and table. The study result showed that the major sources of solid wastes were commercial, household and municipal while incineration and open dumping were the widely practiced solid waste disposal methods. Most of the households (58.13%) were used open dumping method using open space storing while 34.88% households were used incineration method to store solid wastes. And the rest (6.97%) households were used open dumping until they can pay for transportation and use incineration if they can’t. conclusion the sources of solid waste in the study area were commercial, household, municipal and agricultural. Generally, there were problems associated with collection, transportation, safe disposal site and segregation of solid wastes. As a result of improper disposal of solid wastes, there were occurrence of diseases that affect health of the community and result in environmental pollution. Therefore, there is a need to improve the present solid waste disposal and management system so as to ensure sustainable development through creating clean and safe working environment and improving health of the community.

In indeterminate and inconsistent situations, simplified neutrosophic sets (SNSs) contain the single-valued and interval neutrosophic sets described by the truth, falsity, and indeterminacy degrees, while a neutrosophic number (NN) (p =  + I for ,    and I  [IL, IU]) consists of both its certain part  and its uncertain parts I. Owing to the indeterminacy, incompleteness, and inconsistency of decision makers’ arguments in complicated decision making problems, the truth, falsity, and indeterminacy degrees given by them may imply the partial certainty and partial uncertainty information. In this case, either SNS or NN cannot express the uncertainty degrees of the truth, falsity, indeterminacy arguments. To depict the hybrid information of SNS and NN together, this study presented a simplified neutrosophic indeterminate set (SNIS) to describe the hybrid information of both SNS and NN, and then introduced the q-indeterminate correlation coefficients of SNISs with indeterminate degrees of q  [0, 1]. Next, a simplified neutrosophic indeterminate multicriteria decision making method using the q-indeterminate correlation coefficients of SNISs is established along with the small risk (q = 0), moderate risk (q = 0.5), and large risk (q = 1) of decision makers to carry out multicriteria decision making problems in SNIS setting. Eventually, the proposed decision making approach is applied in an example on selecting a satisfactory open pit slope design scheme for an open pit mine in SNIS setting to indicate its practicality and flexibility in SNIS setting.