NDA | Mathematics | Matrices

If A = , then what is A(adj A) equal to?

For what value of k is the matrix  singular?

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

1). AB = BA

2). AB is a scalar matrix

3). AB can be a null matrix

Select the correct answer using the code given below:

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?

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

Select the correct answer using the code given below: