If A and B are square matrices of order ' 3 ' such that A adj (2 B)=16 I 3 and operatornamedet(B)=2 then which of the following is/are true (Where adj ( X ) denotes adjoint of matrix ( X ), X -1 denotes inverse of matrix ( X ) ) and operatornamedet( X ) denotes determinant value of matrix ( X ).

Question

If A and B are square matrices of order ' 3 ' such that A adj (2 B)=16 I 3 and operatornamedet(B)=2 then which of the following is/are true (Where adj ( X ) denotes adjoint of matrix ( X ), X -1 denotes inverse of matrix ( X ) ) and operatornamedet( X ) denotes determinant value of matrix ( X ). (A) ( A -1( operatornameadj( B ))-1=4 A 2. (B) (A-1( operatornameadj( B ))-1= B 2. (C) B ( operatornameadj A )=8 I 3 (D) B( operatornameadj A)=4 I3

Tardigrade Admin · Accepted Answer

Correct answer is (b) (A-1( operatornameadj( B ))-1= B 2.Correct answer is (c) B ( operatornameadj A )=8 I 3

Q. If $A$ and $B$ are square matrices of order ' 3 ' such that $A$ adj $(2 B) = 16 I_{3}$ and $det (B) = 2$ then which of the following is/are true (Where adj $(X)$ denotes adjoint of matrix $(X), X^{- 1}$ denotes inverse of matrix $(X)$ ) and $det (X)$ denotes determinant value of matrix $(X)$ .

$(A^{- 1} (adj (B))^{- 1} = 4 A^{2}$

$(A^{- 1} (adj (B))^{- 1} = B^{2}$

$B (adj A) = 8 I_{3}$

$B (adj A) = 4 I_{3}$

Correct answer is (b) $(A^{- 1} (adj (B))^{- 1} = B^{2}$ Correct answer is (c) $B (adj A) = 8 I_{3}$

Q. If A and B are square matrices of order ' 3 ' such that A adj (2B)=16I3​ and det(B)=2 then which of the following is/are true (Where adj (X) denotes adjoint of matrix (X),X−1 denotes inverse of matrix (X) ) and det(X) denotes determinant value of matrix (X).

(A−1(adj(B))−1=4A2

(A−1(adj(B))−1=B2

B(adjA)=8I3​

B(adjA)=4I3​