If A and B be symmetric matrices of same order, then AB - BA will be a

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3 and 4 .Determinants and Matrices

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If $A$ and $B $ be symmetric matrices of the same order, then $AB - BA$ will be a

A

Symmetric matrix

B

Skew symmetric matrix

C

Null matrix

D

None of these

Solution

(b) Since $A,B$ are symmetric $ \Rightarrow $ $A = A'$ and $B = B'$

$\therefore $ $(AB – BA)' = (AB)' – (BA)' = B'A' – A'B'$

$ = – (A'B' – B'A') = – (AB – BA)$

$ \Rightarrow $ $(AB – BA)$ is skew-symmetric.

Standard 12

Mathematics

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