You can do that with layer overrides. First, set layer 1 to on and layer 2 to off. Then create a new layer containing all the objects in the scene. Right click the enable checkbox of each material layer and select "create layer override". Disable layer 1 and enable layer 2. Use Camera_A in the default render layer and Camera_B in the layer with the overrides. You can then select which render layer is active in the render settings.
Sometimes the "create layer override" option doesn't show up in the menu. This is a Maya issue, but there's a simple workaround: instead of doing it through the menu, you can run this command:
Code: Select alleditRenderLayerAdjustment "maxwellLayer1.enabled"
Make sure to replace "maxwellLayer1" with the name of the material layer you want to change. You can find that out by clicking the enable checkbox and looking in the script editor, where Maya will show the MEL command which corresponds to the enable/disable action, e.g. setAttr "maxwellLayer2.enabled" 1.