**ABSTRACT**

Over the years, the generally accepted fact is that the Sarrus’s rule which was developed by a French Mathematician, P. F. Sarrus in 1833, is only limited to finding the determinant of *3 × 3* Matrices. However, in my previous work [1] “*On the Extension of Sarrus’ Rule to **n × n (n > 3) **Matrices: Development of New Method for the Computation of the Determinant of **4 × 4** Matrices*” which was published in International Journal of Engineering Mathematics, vol. 2016, 14 pages, the possibility of extending the Sarrus’s rule to find the determinant of 4 × 4 matrices was displayed using the newly established Gbemi’s method. The simplicity, accuracy, ease of applications as well as comparatively low computational time and cost of the proposed Gbemi’s method were pointed out. In this further study, additional nine methods of extending the Sarrus’s rule to evaluate the determinant of 4 × 4 matrices are established. The further establishes the effectiveness, consistency for handy calculations, high accuracy and relatively low computational time of the new method. Therefore, with the aid of the generalized extended method* to **n × n*, it could be stated that method will greatly reduce the computational and running time of most software that are largely based on matrices. Consequently, this will greatly reduce the computational cost.

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