If A is diagonal matrix of order 3× 3 is commutative with every square matrix of order 3× 3 under multiplication and trace (A)=12 , then |A| is equal to :-

Question

If A is diagonal matrix of order 3× 3 is commutative with every square matrix of order 3× 3 under multiplication and trace (A)=12 , then |A| is equal to :- (A) 64 (B) 16 (C) 12 (D) 0

Tardigrade Admin · Accepted Answer

A diagonal matrix is commutative with every square matrix if it is a scalar matrix i.e. all diagonal elements are equal. So every diagonal element is 4 and thus |A|=43=64

Q. If A is diagonal matrix of order $3 \times 3$ is commutative with every square matrix of order $3 \times 3$ under multiplication and trace $(A) = 12$ , then $∣ A ∣$ is equal to :-

$64$

$16$

$12$

$0$

A diagonal matrix is commutative with every square matrix if it is a scalar matrix i.e. all diagonal elements are equal. So every diagonal element is $4$ and thus $∣ A ∣ = 4^{3} = 64$

Q. If A is diagonal matrix of order 3×3 is commutative with every square matrix of order 3×3 under multiplication and trace (A)=12 , then ∣A∣ is equal to :-

64

16

12

0

A diagonal matrix is commutative with every square matrix if it is a scalar matrix i.e. all diagonal elements are equal. So every diagonal element is 4 and thus ∣A∣=43=64

Q. If A is diagonal matrix of order $3 \times 3$ is commutative with every square matrix of order $3 \times 3$ under multiplication and trace $(A) = 12$ , then $∣ A ∣$ is equal to :-

$64$

$16$

$12$

$0$

A diagonal matrix is commutative with every square matrix if it is a scalar matrix i.e. all diagonal elements are equal. So every diagonal element is $4$ and thus $∣ A ∣ = 4^{3} = 64$