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(B) Statement $(i)$: $AB=0$ does not necessarily imply $A=0$ or $B=0$. For example,consider two non-zero matrices $A = \begin{bmatrix} 0 & 1 \ 0 & 0

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(ii) is true and $(i)$,(iii) are false

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(B) Statement $(i)$: $AB=0$ does not necessarily imply $A=0$ or $B=0$. For example,consider two non-zero matrices $A = \begin{bmatrix} 0 & 1 \ 0 & 0 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}$. Their product is $AB = \begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix} = 0$. Thus,$(i)$ is false.Statement (ii): If $AB=I_3$,then by the definition of an inverse matrix,$B$ is the inverse of $A$ (i.e.,$A^{-1}=B$). Thus,(ii) is true.Statement (iii): The expansion $(A-B)^2 = (A-B)(A-B) = A^2 - AB - BA + B^2$. Since matrix multiplication is not commutative in general $(AB 
eq BA)$,$A^2 - AB - BA + B^2$ is not equal to $A^2 - 2AB + B^2$ unless $AB=BA$. Thus,(iii) is false.Therefore,only (ii) is true.

If $A$ and $B$ are both $3 \times 3$ matrices,then which of the following statements are true?
$(i)$ $AB=0 \Rightarrow A=0$ or $B=0$
(ii) $AB=I_3 \Rightarrow A^{-1}=B$
(iii) $(A-B)^2=A^2-2AB+B^2$

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If $A$ and $B$ are both $3 \times 3$ matrices,then which of the following statements are true?$(i)$ $AB=0 \Rightarrow A=0$ or $B=0$(ii) $AB=I_3 \Rightarrow A^{-1}=B$(iii) $(A-B)^2=A^2-2AB+B^2$