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 ?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Answer

B

Explanation

If A' = A where A' is transpose of matrix then |A|=|A'| But is not necessary that |A| = 0
i.e. A is singular matrix
Hence, statement 1 is wrong.
Given `A^(3) = I`
`|A^(3)=|I|=1`
`rArr |A| = 1`
Thus, A is non-singular matrix.
Hence, only statement 2 is correct.