If A is a skew symmetric matrix and n is odd positive integr... | MATH - TYPES OF MATRICES, ALGEBRA OF MATRICES | SolveeIt | Solveeit

Today, August 19

Question

If A is a skew symmetric matrix and n is odd positive integer then Aⁿ is –

A

Symmetric matrix

B

Diagonal matrix

C

Skew symmetric matrix

D

None of these

Answer

Skew symmetric matrix

Explanation

Solution

A^T = – A

(Aⁿ)^T = (A A …. A)^T = (A^T A^T … A^T) = (A^T)ⁿ

= (– A)ⁿ

= – A

Hence skew symmetric matrix.