If D_1 and D_2 are two 3 3 diagonal matrices, then - Vidyadip

MCQ

If $D_1$ and $D_2$ are two $3 \times 3$ diagonal matrices, then

A
$D_1D_2$ is a diagonal matrix
B
$D_1D_2 = D_2D_1$
C
$D_1^2 + D_2^2$ is a diagonal matrix
✓
All of the bove

✓

Answer

Correct option: D.

All of the bove

d
Let $D_1 =$ $\left[ {\begin{array}{*{20}{c}}{{x_1}}&0&0\\0&{{y_1}}&0\\0&0&{{z_1}}\end{array}} \right]$ and $D_2 =$ $\left[ {\begin{array}{*{20}{c}}{{x_2}}&0&0\\0&{{y_2}}&0\\0&0&{{z_2}}\end{array}} \right]$, when $x_1 , y_1 , z_1 , x_2 , y_2 , z_2 \neq 0$
then $D_1D_2 = D_2D_1$

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