Fill in the blanks in each of the
If A is a symmetric matrix, then A³ is a ______ matrix.

Question

Fill in the blanks in each of the If A is a symmetric matrix, then A 3 is a ______ matrix.

Philoid · Accepted Answer

A³ is Also a symmetric matrix.

Given: A’=A ..(1)

⇒ (A²)’=(AA)’=A’A’

⇒ A’A’=(A)(A)=A²

⇒ (A²)’=A² (symmetric matrix) ..(2)

⇒ (A³)’=(A(A²))’=(A²)’A’

⇒ (A²)’A’=A²A= A³ (Using (1) and (2) )

⇒ (A³)’=A³ (symmetric matrix)

Fill in the blanks in each of theIf A is a symmetric matrix, then A3 is a ______ matrix.