Let A be a non-singular matrix and B = adj A. Which of the following statements is/are correct?

1. AB = BA

2. AB is a scalar matrix

3. AB can be a null matrix

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Consider the following statements in respect of square matrices A and B of same order :

1. If AB is a null matrix, then at least one of A and B is a null matrix.

2. If AB is an identity matrix, then BA = AB.

Which of the above statements is/are correct?

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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