Prove: If A and B are n times n diagonal matrices, then AB = BA.

permaneceerc 2020-11-05 Answered
Prove: If A and B are n×n diagonal matrices, then
AB = BA.
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Expert Answer

Asma Vang
Answered 2020-11-06 Author has 93 answers
Step 1
Given, A and B are n×n diagonal matrices
Step 2
Suppose
A=[a1100ca220000ann],B=[b11000b220000bnn]
Now
L.H.S.=AB
=[a1100ca220000ann][b11000b220000bnn]
=[a11b11000a22b220000annbnn]
Now
R.H.S.=BA
=[b11000b220000bnn][a1100ca220000ann]
=[b11a11000b22a220000bnnann]
=[a11b11000a22b220000annbnn]
Thus AB=BA
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Jeffrey Jordon
Answered 2022-01-23 Author has 2047 answers

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