Consider the following statements
1. If A' = A, then A is a singular matrix, where A' is the transpose of A.
2. If A is a square matrix such that `A^(3) = I`, then A is non-singular.
Which of the statements guven above is/are correct ?

Consider the following statements: I. If A=A. then A is singular matrix where A is the transpose of A. II. If A is a square matrix such that A^(3)=1 , then A is non-singular. Which of the above statement is/are correct ?

If A is a square matrix such that A^(3)=I , then prove that A is non-singular

Consider the following statements. I. The inverse of a square matrix, if it exists, is unique. II. If A and B are singular matrices of order n, then AB is also a singular matrix of order n. Which of the statements given above is/are correct ?

If A is a non-singular matrix then |A^(-1)| =

If A is non singular matrix of order 3 , then the rank of A =

Consider the following statements. I. The inverse of the square matrix, if it exits, is unique. II. If A and B are singular matrices of order n. then AB is also a singular matrix of order n. Which of the statements given above is/are correct ?

If A is a square matrix such that a_(ij)=(i+j)(i-j), then for A to be non-singular the order of the matrix can be .

If A is a non-singular square matrix such that A^(2)-7A+5I=0, then A^(-1)

If A is non-singular matrix of order 3 ,then the rank of A=

If is a non-singular matrix, then det (A^(1))=