Given, $$ cofactors(b_{ij})= c_{ij} \Rightarrow Adj(B)= C^T $$ \
$$ cofactors(a_{ij})= b_{ij} \Rightarrow Adj(A)= B^T $$ \
$$ det(A) = 2 $$
and the order of the matrices is 3 .
We have to apply the followings :
$$ Adj(A) = (A)^{order(A) – 1} $$
$$ A = A^T $$
$$ ABC = A B C $$
$$ cA = c^{order(A)}A $$
So now $$ Adj(A) = 2^{31}=B^T=B $$ \
$$ Adj(B) = (2^{31})^{31}=C^T=C = 2^4$$
$$ 2A = 2^{3}A = 2^4 $$
Therefore , $$ \displaystyle 2AB^TC = 2A B^T C = 2^4 . 2^2 . 2^4 = \sum_{r=1}^{11} {10 \choose r1} $$

This reply was modified 3 months, 1 week ago by Jatin Kr Dey.

This reply was modified 3 months, 1 week ago by Jatin Kr Dey.

This reply was modified 3 months, 1 week ago by Jatin Kr Dey.

This reply was modified 3 months, 1 week ago by Jatin Kr Dey.

This reply was modified 3 months, 1 week ago by Jatin Kr Dey.

This reply was modified 3 months, 1 week ago by Jatin Kr Dey.