Question-3

If all the elements of a \(n\times n\) matrix \(A\) are the same, find the determinant of \(A\) and \(A+A^{T}\).

---

We can perform the row operation \(R_{1}\rightarrow R_{1}-R_{2}\). This would leave the determinant unchanged and will result in a zero row. Thus \(|A|=0\). Since \(A+A^{T}=2A\) for this matrix, \(|A+A^{T}|=0\).