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Question

If A=152271391 and B=411123501, then verify that

(i)(A+B)T=AT+BT
(ii)(AB)T=ATBT

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Solution

We have:
AT=152271391BT=411123501
(i) A+B=152271391+411123501
(A+B)=532699142
AT+BT=123579211+415120131=561394292

Hence, we have verified that (A+B)T=AT+BT
(ii) AB=152271391411123501
(AB)T=318459320
ATBT=152271391411123501=318459320
Hence, we have proved that (AB)T=ATBT.

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