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?

NDA 2025 Mathematics question

Consider the following in respect of non-singular matrices and : I. II. , where is the identity matrix III. How many of the above are correct?

Answer: (A)

The correct reversal laws are and ; since matrix multiplication is not commutative, I and III

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Question ID VK-030146