If A   is a 3 × 3 non-singular matrix such that A A ' = A ' A and B = A - 1 A ' , then B B ' equals, where X ' denotes the transpose of the matrix X .

Question

If A &#160; is a 3 &#215; 3 non-singular matrix such that A A ' = A ' A and B = A - 1 A ' , then B B ' equals, where X ' denotes the transpose of the matrix X .

Aicharya · Accepted Answer

A ' = A T A A ' = A ' A B = A - 1 A ' B ' = A - 1 A ' ' = A ' ' &#183; A - 1 ' = A A - 1 ' B B ' = A - 1 A ' &#183; A A - 1 ' = A - 1 &#183; A &#183; A ' &#183; A - 1 ' &#8757;&#160;&#160; A A ' = A ' A = I &#183; A ' &#183; A - 1 ' = I &#183; A - 1 A ' &#8757;&#160;&#160; C D ' = D ' C ' = I &#183; I ' = I 2 &#8757;&#160;&#160; I = I ' = I

If A   is a 3 × 3 non-singular matrix such that A A ' = A ' A and B = A - 1 A ' , then…

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