® A system of equation is consistent or inconsistent according as its solution
exists or not ® For a square matrix A in matrix equation AX = B
(i) |A| ≠ 0, there exists unique solution
(ii) |A| = 0 and (adj A) B ≠ 0, then there exists no solution
(iii) |A| = 0 and (adj A) B = 0, then system may or may not be consistent Rationalised 2023-24
DETERMINANTS     103
Historical Note
The Chinese method of representing the coefficients of the unknowns of
several linear equations by using rods on a calculating board naturally led to the
discovery of simple method of elimination The arrangement of rods was precisely
that of the numbers in a determinant