Let be any square matrix. It turns out that the determinant of is equal to . Here , the trace of , is the sum of the entries of on the main diagonal.
Keeping this in mind which of the following is definitely not true?

Question

Let be any square matrix. It turns out that the determinant of is equal to . Here , the trace of , is the sum of the entries of on the main diagonal.

Keeping this in mind which of the following is definitely not true?

Answer

is a positive number.

Answer

The column vectors of    are linearly independent.

Answer

The determinant of    is a matrix of the same dimensions as   .

Answer

The reduced row echelon form of    is the identity matrix.

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