Continuing with my matrix multiplication question, I want to show the following expression in explicit viewable form in mma:

Even if in the case I give a11, ..., b11, ... explicit numbers, I still want it to be (0&&1)||(1&&1) in unevaluated form. Can anyone please help?
Use
Inner[And, Array[Subscript[a, ##] &, {2, 2}],
Array[Subscript[b, ##] &, {2, 2}], Or] // MatrixForm

Edit. Having followed up on your previous question, I think you might consider
Inner[HoldForm[And[##]] &, amat,
bmat, HoldForm[Or[##]] &] // MatrixForm

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