Question

The product of two diagonal matrices is always a :-

• A. row matrix.
• B. identity matrix.
• C. scalar matrix.
• D. diagonal matrix.

Answer 1

The correct option is D diagonal matrix.

$\mathrm{Let}A=\left(\begin{array}{ccc}a& 0& 0\\ 0& b& 0\\ 0& 0& c\end{array}\right]\mathrm{and}B=\left(\begin{array}{ccc}l& 0& 0\\ 0& m& 0\\ 0& 0& n\end{array}\right]A\times B=\left(\begin{array}{ccc}\mathrm{al}& 0& 0\\ 0& \mathrm{bm}& 0\\ 0& 0& \mathrm{cn}\end{array}\right]\mathrm{which}\mathrm{is}a\mathrm{diagonal}\mathrm{matrix}.$