Sub multiplicative property of infinity norm is equality

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Let, $\mathbf{A}$ and $\mathbf{B}$ be $n \times n$ matricies. When is it true that, $$||\mathbf{A}\mathbf{B}||_{\infty} = ||\mathbf{A}||_{\infty}||\mathbf{B}||_{\infty}? $$

Or is it always true? Thanks.