Question

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

• A. $Adj (AB) = (Adj A) \,(Adj B)$
• B. $(A + B)^{-1} = A^{-1} + B^{-1}$
• C. AB = 0 $\Rightarrow$ | A | = 0 or | B | = 0
• D. AB = 0 $\Rightarrow$ | A | = 0 and | B | =0.

Answer 1

Answer: (B)

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

Answer 2

AB = 0 $\Rightarrow$ | A | = 0 or | B | = 0