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Question

If A is a square matrix ⎡⎢⎣123456789⎤⎥⎦ then A+AT is a symmetric matrix.


A

True

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B

False

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Solution

The correct option is A

True


A=123456789, AT=147258369

Now A+AT will be obtained by adding corresponding elements of A and AT

So A+AT=261061014101418

Now if we take the transpose of A+AT it will come out to be A+AT=261061014101418 which is same as A+AT. So A+AT is a symmetric matrix.

Here please note thatif A is a square matrix A+AT is always a symmetric matrix. It is not the case only with this particular example. It is rather a property of a square matrix which states that if A is a square matrix then A+AT will always be a symmetric matrix.


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