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Question

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

A
D1D2 is a diagonal matrix
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B
D1+D2 is a diagonal matrix
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C
D21+D22 is a diagonal matrix
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D
1, 2, 3 are correct
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Solution

The correct option is D 1, 2, 3 are correct
If D1 and D2 are diagonal matrix then
D1D2,D1+D2 is also a diagonal matrix.
A=⎢ ⎢ ⎢a11a22.ann⎥ ⎥ ⎥

B=⎢ ⎢ ⎢l11l22.lnn⎥ ⎥ ⎥

then,
AB=⎢ ⎢ ⎢a11l11a22l22.annlnn⎥ ⎥ ⎥

A+B=⎢ ⎢ ⎢a11+l11a22+l22.ann+lnn⎥ ⎥ ⎥

A2=⎢ ⎢ ⎢ ⎢a211a222.a2nn⎥ ⎥ ⎥ ⎥

D21+D22 is also a diagonal matrix.

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