An upper triangular matrix is an n × n matrix whose entries below the main diagonal are...

An upper triangular matrix is an n × n matrix whose entries below the main diagonal are all zero. (Note: The main diagonal is the diagonal going from upper left to lower right.) For example, the matrix

is upper triangular. (a) Give an analogous definition for a lower triangular matrix and also an example of one. (b) Use cofactor expansion to show that the determinant of any n × n upper or lower triangular matrix A is the product of the entries on the main diagonal. That is, det A = a₁₁a₂₂ · · · a_nn.