If all the diagonal entries of an matrix are odd integers and all the other entries are even integers, then must be an invertible matrix.
Therefore, A is invertible. So, the given statement is true.
Using the definition of , the product in the addend corresponding to the diagonal pattern is odd, while all other addends are even.
Thus, is odd, so it must be different than 0.
Thus, is invertible. So, the given statement is true.
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