Is the zero matrix upper and lower triangular as well as diagonal?
Solution 1:
A zero square matrix is lower triangular, upper triangular, and also diagonal.
Solution 2:
Provided it is a square matrix.
An upper triangular matrix is one in which all entries below the main diagonal are zero. Clearly this is satisfied.
A lower triangular matrix is one in which all entries above the main diagonal are zero. Clearly this is satisfied.
A diagonal matrix is one in which all non-diagonal entries are zero. Clearly this is also satisfied.
Hence, a zero square matrix is upper and lower triangular as well as a diagonal matrix.