Question

THEOREM

(a) The transpose of a lower triangular matrix is upper triangular, and the transpose

of an upper triangular matrix is lower triangular.

(b) The product of lower triangular matrices is lower triangular, and the product of

upper triangular matrices is upper triangular.

(c) A triangular matrix is invertible if and only if its diagonal entries are all nonzero.

(d) The inverse of an invertible lower triangular matrix is lower triangular, and the

inverse of an invertible upper triangular matrix is upper triangular.

for all a,b,c and d, can you please give the proof for b only with JUSTIFICATION AND EXPLANATION. short proofs if necessary please.

Answer 1