Which of the following statements are true:

1. Every identity matrix, I of order n is an upper triangular matrix.

2. Every identity matrix, I of order n is a lower triangular matrix.

Concept:

Upper triangular matrix:

Any square matrix, whose every element below the principal diagonal are zero is said to be an upper triangular matrix.

Ex: Here, we have a matrix A of order 3, A = \(\left( {\begin{array}{*{20}{c}} a&b&c\\ 0&e&d\\ 0&0&f \end{array}} \right)\), where a, b, c, d, e and f ∈ R is an upper triangular matrix.

Lower Triangular matrix:

Any square matrix, whose every element above the principal diagonal are zero is said to be a lower triangular matrix.

Ex: Here, we have a matrix A of order 3, A = \(\left( {\begin{array}{*{20}{c}} a&0&0\\ b&e&0\\ c&d&f \end{array}} \right)\), where a, b, c, d, e and f ∈ R is a lower triangular matrix.

Identity Matrix:

Any square matrix, whose principal diagonal elements are one and rest of the elements are zero is said to be an identity matrix.

Ex: Here, we have a matrix A of order 3, I = \(\left( {\begin{array}{*{20}{c}} 1&0&0\\ 0&1&0\\ 0&0&1 \end{array}} \right)\), is an identity matrix.

∴ Identity is Upper triangular matrix and Lower Triangular matrix both