Consider the following in respect of a non-singular matrix M: I. |M^{2}|=|M|^{2} II. |M|=|M^{-1}| III. |M|=|M^{T}| How many of the above are correct?

Explanation

Statement I is true because |AB| = |A||B|. Statement III is true because a matrix and its transpose share the same determinant. Statement II is false in general since |M^{-1}| = \frac{1}{|M|}. Therefore, exactly two statements are correct.

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