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College Mathematics Linear Algebra Examination Questions
Aij is the algebraic cofactor of Aij, which is defined as follows:

Cross out the row and column of aij in A, and multiply the remaining determinant by (-1) (I+J).

For example, A21= (-1) (1+2) in your question is multiplied by the following determinant.

2 3

4 3

= (- 1)*(2*3 - 3*4) = 6