Consider the following statements:
1. If product of the matrix \(B=\begin{pmatrix} 2 & 6 &4 \\ 1& 0&1 \\ -1&1 & -1 \\ \end{pmatrix}\) with a matrix A inverse has \(C=\begin{pmatrix} -1 & 0 &1 \\ 1& 1&3 \\ 2&0 & 2 \\ \end{pmatrix}\), then \(A^{-1}=\begin{pmatrix} -3 & -5 &-5 \\ 0& 9&2 \\ 2&14& 6 \\ \end{pmatrix}\)
2. If a square matrix A is orthogonal as well as symmetric, then A is an idempotent matrix.
Which of the above statements is/are correct?
1
1 only
2
2 only
3
Both 1 and 2
4
Neither 1 nor 2