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

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_(ij)=(i+j)(i-j), then for A to be non-singular the order of the matrix can be .

If S is a real skew-symmetric matrix, then prove that I-S is non-singular and the matrix A=(I+S)(I-S)^(-1) is orthogonal.

If S is a real skew-symmetric matrix, then prove that I-S is non-singular and the matrix A=(I+S)(I-S)^(-1) is orthogonal.

If S is a real skew-symmetric matrix, then prove that I-S is non-singular and the matrix A=(I+S)(I-S)^(-1) is orthogonal.

If S is a real skew-symmetric matrix, then prove that I-S is non-singular and the matrix A=(I+S)(I-S)^(-1) is orthogonal.

If S is a real skew-symmetric matrix, then prove that I-S is non-singular and the matrix A=(I+S)(I-S)^(-1) is orthogonal.

If A is a non-singular matrix, then

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