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
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
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