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Home / Doubts and Solutions/ICSE/Class 12 Science/Mathematics

If A is square matrix, prove that A'A is Symmetric.

Asked by drawing13334 30th August 2018, 3:21 PM
Answered by Expert
Answer:
begin mathsize 16px style Symmetric space Matrix colon If space straight B to the power of straight T space equals space straight B space then comma space apostrophe straight B apostrophe space is space straight a space symmetric space matrix Here space we space have space to space prove space that space straight A to the power of straight T straight A space is space symmetric. means space to space prove space that space open parentheses straight A to the power of straight T straight A close parentheses to the power of straight T space equals space straight A to the power of straight T straight A space open parentheses straight A to the power of straight T straight A close parentheses to the power of straight T space equals space open parentheses straight A close parentheses to the power of straight T open parentheses straight A to the power of straight T close parentheses to the power of straight T space..... by space reversal space law space space space space space space space space space space space space space space equals space open parentheses straight A close parentheses to the power of straight T straight A space space space space space space space space space space space space space space space equals space straight A to the power of straight T straight A Hence space proved. end style
Answered by Expert 30th August 2018, 5:16 PM
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