Question

Prove that if AB= 0and A is invertible then B= 0

Answer 1

Answer with Step-by-step explanation:

Since we have given that

AB = 0 and A is invertible so, AA⁻¹ = I

So, Consider,

$AB=0$

Multiplying A⁻¹ on both the sides, we get that

$A^{-1}AB=A^{-1}0\\\\(AA^{-1})B=0\\\\IB=0\\\\B=0$

Hence proved.