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Determinant. “The determinant of an equivalent matrix” defined as det(M) for M of size q × q can be designed recursively as given below [5].

 • If q = 1, det(M) = m11.

 • If q > 1, .

where Mij stands for a matrix M defined by ith row and jth column. The determinant may be found only for an equivalent matrix.

Additive Inverse. If matrix N is “the additive inverse” of matrix M, then M + N = 0 because their corresponding elements have the property: nij = −mij for all i’s and j’s. The symbol –M is generally used to represent the additive inverse of matrix M [5].

Multiplicative Inverse. Only square matrices can be used to compute “the reciprocal of a matrix”. Matrix M has a reciprocal of N, resulting in M × N = N × M = I. The symbol M-1 is generally used to represent a reciprocal of M. The matrices have their reciprocals in the case of det(M) ≠ 0 [5].