Consider the following in respect of non-singular matrices A and B : I. (AB)^{-1}=A^{-1}B^{-1} II. (BA)(AB)^{-1}=I, where I is the identity matrix III. (AB)^T=A^TB^T How many of the above are correct?

Explanation

Statement I is incorrect because the reversal law states (AB)^{-1} = B^{-1}A^{-1}. Statement II evaluates to (BA)B^{-1}A^{-1} = B(AB^{-1})A^{-1}, which does not generally simplify to the identity matrix unless A and B commute. Statement III is incorrect because the transpose also follows the reversal law: (AB)^T = B^T A^T. None of the statements are correct.

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