If A is the identity matrix of order 3 and B is its transpose, then what is the value of the determinant of the matrix C = A + B?

Let A and B be non-singular matrices of the same order such that AB = A and BA = B. Which of the following statements is/are correct ?

1. A² = A

2. AB² = A²B

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How many terms are there in the expansion of $\left(1 + \frac{2}{x}\right)^9\left(1-\frac{2}{x}\right)^9 ? $

Consider the following statements in respect of the expansion of (x + y)¹⁰

1. Among all the coefficients of the terms, the coefficient of the 6th term has the highest value

2. The coefficient of the 3rd term is equal to coefficient of the 9th term

Which of the above statements is /are correct ?