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Question

If D1 and D2 are two 3×3 diagonal matrices, then

A
D1D2 is diagonal matrix
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B
D1D2=D2D1
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C
D21+D22 is a diagonal matrix
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D
none of these
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Solution

The correct options are
A D21+D22 is a diagonal matrix
C D1D2 is diagonal matrix
D D1D2=D2D1
Let D1=a000b000c,D2=x000y000z
Then
D1D2=a000b000cx000y000z=ax000by000cz


D2D1=x000y000za000b000c=xa000yb000zc
As ax=xa,by=yb,cz=zc
D1D2=D2D1
D12+D22=a000b000ca000b000c+x000y000zx000y000z

=a2000b2000c2+x2000y2000z2=⎢ ⎢ ⎢a2+x2000b2+y2000c2+z2⎥ ⎥ ⎥

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