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If D(1) and D(2) are two 3x3 diagnal mat...

If `D_(1) and D_(2)` are two `3x3` diagnal matrices where none
of the diagonal elements is zero, then

A

`D_(1) D_(2)` is a diagonal matrix

B

`D_(1) D_(2) = D_(2)D_(1)`

C

`D_(1)^(2)+D_(2)^(2)` is a diagonal matrix

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Let `D_(1) = [[d_(1),0,0],[0,d_(2),0],[0,0,d_(3)]] and D_(2) = [[d_(4),0,0],[0,d_(5),0],[0,0,d_(6)]]`
`therefore D_(1)D_(2) [[d_(1)d_(4),0,0],[0,d_(2)d_(5),0],[0,0,d_(3)d_(6)]] = D_2D_1`
`andD_(1)^(2) + D_(2)^(2) = [[d_(1)^(2),0,0],[0,d_(2)^(2),0],[0,0,d_(3)^(2)]] + [[d_(4)^(2),0,0],[0,d_(5)^(2),0],[0,0,d_(6)^(2)]]`
` = [[d_(1)^(2)+d_(4)^(2),0,0],[0,d_(2)^(2)+d_(5)^(2),0],[0,0,d_(3)^(2)+d_(6)^(2)]] `
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