Solution:
Given, the value of a third order determinant is 11. Let the determinant be represented by |A|.
We are to find the value of the square of the determinant formed by the co-factors of A.
Let |C| be the determinant formed by co-factors of A.
We know that the value of |C| is given by:
|C| = a11*A11 + a12*A12 + a13*A13
where aij is the co-factor of the element Aij.

Calculation of co-factors of A:
Let A =
|a11 a12 a13|
|a21 a22 a23|
|a31 a32 a33|

The co-factor of aij is given as:
aij = (-1)^(i+j) Mij
where Mij is the determinant formed by deleting the ith row and jth column of A.

Using this formula, we can calculate the co-factors of A as follows:
a11 = (-1)^(1+1) * (a22*a33 - a23*a32) = a22*a33 - a23*a32
a12 = (-1)^(1+2) * (a21*a33 - a23*a31) = -(a21*a33 - a23*a31) = a23*a31 - a21*a33
a13 = (-1)^(1+3) * (a21*a32 - a22*a31) = a21*a32 - a22*a31
a21 = (-1)^(2+1) * (a12*a33 - a13*a32) = -(a12*a33 - a13*a32) = a13*a32 - a12*a33
a22 = (-1)^(2+2) * (a11*a33 - a13*a31) = a11*a33 - a13*a31
a23 = (-1)^(2+3) * (a11*a32 - a12*a31) = -(a11*a32 - a12*a31) = a12*a31 - a11*a32
a31 = (-1)^(3+1) * (a12*a23 - a13*a22) = a12*a23 - a13*a22
a32 = (-1)^(3+2) * (a11*a23 - a13*a21) = -(a11*a23 - a13*a21) = a13*a21 - a11*a23
a33 = (-1)^(3+3) * (a11*a22 - a12*a21) = a11*a22 - a12*a21

We can now substitute these values to get |C| as follows:
|C| = a11*A11 + a12*A12 + a13*A13
= (a22*a33 - a23*a32)*a11 + (a23*a31 - a21*a33)*a12 + (a21*a32 - a22*a31)*a13

Calculation of A11, A12, A13:
The co-factor matrix of A is given as follows:
| A11 -A12 A13|
|-A21 A22 -A23|
| A31 -A32 A33|

Using this matrix, we can calculate A11, A12, and A

Wkt,
value of determinant formed by cofactors of determinant=
(∆)^2
so it's square will be (∆)^4
so value of square=(11)^4