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^T B^T How many of the above are correct?

Question

Quantrex Academy · Accepted Answer

Correct answer: A. None

For Statement I, the reversal law of matrix inverse gives (AB)^ -1 = B^ -1 A^ -1 . Since matrix multiplication is not commutative in general, B^ -1 A^ -1 A^ -1 B^ -1 . Thus, Statement I is incorrect. For Statement II, using the reversal law, (BA)(AB)^ -1 = (BA)(B^ -1 A^ -1 ) = B(AB^ -1 )A^ -1 = BIA^ -1 = BA^ -1 . This is not equal to I in general. Thus, Statement II is incorrect. For Statement III, the reversal law of matrix transpose gives (AB)^T = B^T A^T. Since matrix multiplication is not commutative, B^T A^T A^T B^T in general. Thus, Statement III is incorrect. Since none of the statements are correct, the number of correct statements is zero. Answer: None

NDA Mathematics Question (2025) — Solution

Question

Options

Answer

Step-by-step solution