Tricky Matrix

Consider a triangle with vertices as $A(l,p)$ , $B(m,q)$ , and $C(n,r)$ .

From the information given we can see that length of the sides of the triangle are $AB= 3, BC= 4, and CA= 5$ .

We also know that $det(A) = 2 Ar( \Delta ABC)$ .

Therefore $det(B) = (det(A))^{2} = (2 Ar( \Delta ABC))^{2}$

The area of the triangle can be calculated easily as $Ar(\Delta ABC) = 6 sq.units$ .

Hence $det(B) = 4 \times 36 = \boxed{144}$