(1)If an upper triangular n×n matrix R is invertible, prove that its inverse is also upper triangular. (2)If an upper triangular matrix is orthogonal, prove that it must be a diagonal matrix. If A is...

(1)If an upper triangular n×n matrix R is invertible, prove that its inverse is also upper triangular.

(2)If an upper triangular matrix is orthogonal, prove that it must be a diagonal matrix. If A is an invertible n×n matrix and if A=Q1R1=Q2R2,where R1 and R2 are upper triangular with positive diagonal entries and Q1,Q2 are orthogonal, prove that Q1=Q2 and R1=R2.