Square of A is symmetric

by admin
square of A skew symmetric proof

  The document titled Square of A is symmetric explores the symmetry of the square of matrix A. It delves into the mathematical properties and characteristics of the squared matrix, highlighting its symmetrical nature.

If A is symmetric  or skew symmetric  then we show that square of A is symmetric ( A² is symmetric).

Proof.

Consider A is symmetric Then ”   A transpose = A  “……… (1)

Now    A ²  will  be symmetric If  (A ² ) transpose = A ²

square of A symmetric proof

Let A be skew symmetric then A transpose =  -A

Now A ² will be symmetric if ( A ² ) transpose  = A ²

( A ² ) transpose  = A ²

L . H . S  = ( A ² ) transpose

square of A skew symmetric proof

RELATED POST:

Term Monoid in set theory

Define binary operation

singleton set has proper subset