Question

# Which of the following is true for a matrix A.

A

A = AT ⇒ A is skew symmetric

B

A = -AT ⇒ A is skew symmetric

C

is skew symmetric

D

A = -AT ⇒ A is symmetric

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. $$⎡⎢⎣023−201−3−10⎤⎥⎦$$ AT=⎡⎢⎣0−2−320−1310⎤⎥⎦ 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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