Question

Let A, B be square matrix such that A B = 0 and B is non singular then

• A. $\left|A\right|$ must be zero but A may non zero
• B. A must be zero matrix
• C. nothing can be said in general about A
• D. none of these

Answer 1

The correct option is B A must be zero matrix

$A.B=0\Rightarrow A.B.B^{-1}=0.B^{-1}\Rightarrow A.I=0\Rightarrow A=0$