Why can't a triangular matrix with only zeros in its diagonal be invertible?
I know that it is not invertible but I don't know well the reasons, perhaps. Actually, I read that can't have any zero in its diagonal, in order to be invertible.
In general, I know that if a matrix has an inverse, the product of that matrix with its inverse is equal to the identity matrix, namely, with a matrix with 1s as its diagonal.