There exists a matrix whose entries are all 1 or -1 , and such that .
Therefore, the given statement is false.
We know that determinant of similar matrices is equal.
So, det (A) must be equal to, det (2A)which is false.
If A is a matrix with entries -1 or 1 , then all 24 of the addends in the definition of can be either - 1 or 1 .
If we want det A = 16, then twenty of them must be 1, and the remaining four be -1, which is impossible.
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