Let A = [a_ij] be a square matrix of order 3 with |A| = 2 and let C = [c_ij], where c_ij = cofactor of a_ij in A. Then, |C| = ______________.

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Solution

Given:
|A| = 2
Order of A = 3

$As we know, |adj (A)| = {|A|}^{n - 1} where n is the order of A Also, adj (A) = C^{T} \Rightarrow |adj (A)| = |C^{T}| \Rightarrow |adj (A)| = |C| (∵ |C^{T}| = |C|) \Rightarrow {|A|}^{n - 1} = |C| \Rightarrow |C| = {|A|}^{n - 1} \Rightarrow |C| = {|A|}^{3 - 1} (∵ order of A = 3) \Rightarrow |C| = {|A|}^{2} \Rightarrow |C| = 2^{2} (∵ |A| = 2) \Rightarrow |C| = 4$

Hence, |C| = 4.

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Let A = [aij] be a square matrix of order 3 with |A| = 2 and let C = [cij], where cij = cofactor of aij in A. Then, |C| = ______________.

Given: |A| = 2 Order of A = 3 As we know,adjA=An-1 where n is the order of AAlso, adjA=CT⇒adjA=CT⇒adjA=C ∵ CT=C⇒An-1=C⇒C=An-1⇒C=A3-1 ∵ order of A=3⇒C=A2⇒C=22 ∵ A=2⇒C=4 Hence, |C| = 4.

Let A = [a_ij] be a square matrix of order 3 with |A| = 2 and let C = [c_ij], where c_ij = cofactor of a_ij in A. Then, |C| = ______________.