Hello Aspirant,

Here in this, the question is given that A is a square matrix. Aij is the co-factor of aij.

To find - a 21 A 11+ a 22 A 11+a 23 A 13

Solution-

|a 11      a 12    a 13|

|a 21      a 22    a 23|                       = A

|a 31      a 32    a 33|

We are given that Aij is a cofactor of aij.

Hence cofactor of the second column is A21, A22, and A23 respectively.

We know that if we multiply the elements of one row with cofactors of the other row, then their sum will be 0.

So, the sum of a_{21} A_{11} + a_{22 }A_{12} + a_{23} A_{13} = 0.

I hope it helps.

Thank you.