Question

The value of a 3rd order determinant is 11, then the value of the square of the determinant formed by the co-factors will be ?

Answer 1

If A is 3 x 3 matrix
Let C be its co factor matrix
then
$C^{T}A = det(A)I$
[tex]det(C^{T}A) = det(det(A)I) \\ det(C^{T})det(A)=det^{3}(A) \\ det(C)=det(C^{T}) = det^{2}(A)[/tex]
as $det(A) = 11$
$det^{2}(C) = det^{4}(A) = 11^4 = 14641$

Answer 2

Answer:

the value of determinant is 11

the value of determinant formed by cofactor is (det)^n-1

n=3

(11)^3-1= 11^2= 121

their square = (121)^2 =14641

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