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  4. If A is a square matrix. A' its transpose, then (1/2)(A-A') is

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Q. If $A$ is a square matrix. $A'$ its transpose, then $ \frac{1}{2}(A-A') $ is

J & K CETJ & K CET 2008Matrices

Solution:

Now, $ {{\left[ \frac{1}{2}\,(A-A') \right]}^{'}}=\frac{1}{2}(A-A')' $
$ =\frac{1}{2}(A'-A) $
$ =-\frac{1}{2}(A-A') $
Hence, it is a skew symmetric matrix.