If A and B are square matrices of order 3, then

Question

If A and B are square matrices of order 3, then (A)  operatornameadj(A B)= operatornameadj A+ operatornameadj B (B) (A+B)-1=A-1+B-1 (C) A B=O ⇒|A|=0 or |B|=0 (D) A B=O ⇒|A|=0 and |B|=0

Tardigrade Admin · Accepted Answer

If A B=O, then either of A and B is necessarily singular.

Q. If $A$ and $B$ are square matrices of order $3,$ then

$adj (A B) = adj A + adj B$

$(A + B)^{- 1} = A^{- 1} + B^{- 1}$

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

$A B = O \Rightarrow ∣ A ∣ = 0$ and $∣ B ∣ = 0$

If $A B = O,$ then either of $A$ and $B$ is necessarily singular.

Q. If A and B are square matrices of order 3, then

adj(AB)=adjA+adjB

(A+B)−1=A−1+B−1

AB=O⇒∣A∣=0 or ∣B∣=0

AB=O⇒∣A∣=0 and ∣B∣=0