Q14 of 108 Page 100

If the matrix A is both symmetric and skew symmetric, then

Given A is both symmetric and skew symmetric matrix then, A = A’ and also A = -A’

⇒ A’ = -A’


⇒ 2A’ = 0


⇒ A’ = O


Clearly it is observed that transpose of A is a null matrix or zero matrix then matrix A must also be a zero matrix.


Hence A is a zero matrix.

More from this chapter

All 108 →
11

Find the matrix X so that

12

If A and B are square matrices of the same order such that AB = BA, then prove by induction that ABn = BnA. Further, prove that (AB)n = AnBn for all n ϵ N.

 13

If is such that A � = I, then

 15

If A is square matrix such that A2 = A, then (I + A) � – 7 A is equal to