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 = , 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 = , 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 = , is an identity matrix.

∴ Identity is Upper triangular matrix and Lower Triangular matrix both