Question

A diagonal matrix will always be

• A. Rectangular matrix
• B. Identity matrix
• C. Square matrix
• D. None of these

Answer 1

The correct option is D

None of these

A diagonal matrix is defined as a matrix with all non-diagonal elements are zero. For this we should know what a main diagonal is. Main diagonal is set all elements given by a_ii . You can see its possible in rectangular matrix also. See the below example.

$\left[\begin{array}{cc}1& 0\\ 0& 5\\ 0& 0\end{array}\right]$

This rectangular matrix satisfies this condition. Also it may not be always an identity matrix since the main diagonal element can also be elements other than one.

Hence none of the options a, b or c can be a sure case with a general diagonal matrix although a diagonal matrix can also be a rectangular matrix/ square matrix /identity matrix.