Question

If A and B be two square matrices of the same order then | AB | = 0 implies

• A. A = O or B = O
• B. A = O and B = O
• C. | A | = 0 and | B | = 0
• D. | A | = 0 or | B | = 0

Answer 1

The correct option is D | A | = 0 or | B | = 0

So if we assume that $A,B$ Both matrics are non singular i.e. they are inversible because that is the condition for inverse

$A^{-1}AB=B$ $AB{B}^{-1}=A$

$AB$ is zero metrix so $A=B=0$

$A^{-1}\left(0\right)=B$

$B=0=A$

So initial assumption $A,B$ are non singular they are prove flase