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Given the matrices A = [[2, -1], [-7, 4]] and B = [[4, 1], [7, 2]], which of the following statements is correct?

1. AA^T = I
2. BB^T = I
3. AB ≠ BA
4. (AB)^T = I

Correct answer: (AB)^T = I

Solution

AB = [[2,-1],[-7,4]][[4,1],[7,2]] = I, and BA = I too, so AB = BA. Also A A^T != I and B B^T != I. Hence (AB)^T = I^T = I is the correct statement.

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