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Cofactor

If A=[aij] ...

Question

If $A = [a i j]$ is a matrix of order 2x2 such that $| A | = 15$ and cij represents the co factor of aij then find $a_{21} c_{21} + a_{22} c_{22}$ .

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Solution

Determinant of a $2 \times 2$ matrix is given by
$| A | = a_{21} c_{21} + a_{22} c_{22}$
Given, $| A | = 15$
Hence,
$a_{21} c_{21} + a_{22} c_{22} = 15$

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