Consider three non-zero matrices $\text{A}, \text{B}$ and $\text{C}$ such that $\text{ABB}’ = \text{CBB}’$ where $\text{B}’$ is the transpose of $\text{B}$. Which of the following statements is necessarily true?
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$r(\text{A}) =r(\text{C})$
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non-zero eigenvalues of $\text{A}$ and $\text{C}$ are identical.
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$\text{AB = CB}$
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None of the above.
