If A and B are square matrices of order 3× 3, then which of the following is true?

Question

If A and B are square matrices of order 3× 3, then which of the following is true? (A)  AB=0⇒ A=O or B=O  (B)  det(2AB)=8 text (detA) text (detB)  (C)  A2-E2=(A+B)(A-B)  (D)  det(A+B)=det(A)+det(B)

Tardigrade Admin · Accepted Answer

det (2AB) = 23 det[A] det[B] = 8 det[A] det[B]

Q. If A and B are square matrices of order $3 \times 3,$ then which of the following is true?

$A B = 0 \Rightarrow A = O$ or $B = O$

$d e t (2 A B) = 8 (d e t A) (d e tB)$

$A^{2} - E^{2} = (A + B) (A - B)$

$d e t (A + B) = d e t (A) + d e t (B)$

det (2AB) = 23 det[A] det[B] = 8 det[A] det[B]

Q. If A and B are square matrices of order 3×3, then which of the following is true?

AB=0⇒A=O or B=O

det(2AB)=8 (detA) (detB)

A2−E2=(A+B)(A−B)

det(A+B)=det(A)+det(B)

det (2AB) = 23 det[A] det[B] = 8 det[A] det[B]

Q. If A and B are square matrices of order $3 \times 3,$ then which of the following is true?

$A B = 0 \Rightarrow A = O$ or $B = O$

$d e t (2 A B) = 8 (d e t A) (d e tB)$

$A^{2} - E^{2} = (A + B) (A - B)$

$d e t (A + B) = d e t (A) + d e t (B)$