Question-7

Let \(A=[\delta_{ij}]\) be a matrix of order \(3\) such that \(\delta_{ij}=\begin{cases} 0 & \text{if }i>j\\ j & \text{if }i\leq j \end{cases}\). Is \(A\) upper triangular or lower triangular? Find \(\text{det}(A)\).

---

\[ A=\begin{bmatrix}1 & 2 & 3\\ 0 & 2 & 3\\ 0 & 0 & 3 \end{bmatrix} \]

\(A\) is upper triangular as all entries below the main diagonal are zero. \(\text{det}(A)=1\times2\times3=6\), the product of the diagonal entries since \(A\) is upper triangular.