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Question:

If Aij is the cofactor of the element aij of the determinant, then write the value of a32.A32.

Solution:

Given a square matrix, the cofactor of aij is denoted by Aij = (-1)i+jMij, where Mij is the minor of the entry aij.
Mij = |2 5|
|6 4|
From the matrix, a32 = 5
Determinant of A32 = (-1)3+2|2 5|
|6 4|
= - (8 - 30) = 22
Therefore, a32.A32 = 5 × 22 = 110.