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Question

Which of the following is true for a matrix A.



A

A = AT ⇒ A is skew symmetric

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B

A = -AT ⇒ A is skew symmetric

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C

is skew symmetric

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D

A = -AT ⇒ A is symmetric

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Solution

The correct option is B

A = -AT ⇒ A is skew symmetric


We have mentioned in the videos that for a square matrix A, if A=AT then A is said to be a skew symmetric matrix i.e., when we take the transpose of A the new matrix is (-1)x transpose of A.

\(

023201310\)

AT=023201310

Here we can clearly see that in AT all the corresponding elements of A are multiplied by (-1) i.e., A=AT. So this is a skew symmetric matric. So option (b) is correct.


Mathematics

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