Question

Are all upper triangular matricies and lower triangular matrices

always invertible?

If so, I'd like to know the reason!
If not, what are special cases that are invertible?

Thank you in advance.

Answer 1

No, not all upper triangular matrices and lower triangular matrices are always invertible.

Explanation:

I did the test

Hope this helps :)

Answer 2

No, not all upper triangular matrices and lower triangular matrices are always invertible. A triangular matrix (lower or upper) is invertible if and only if all entries of the main diagonal are non-zero.

Explanation: