If A is a skew symmetric matrix then A2 is a _____

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

If A is a skew symmetric matrix then A² is a ______.

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A is a skew symmetric matrix.

So, A' = – A ....(1)

Now,

(A²)' = (A × A)' = A' × A' ..... {∵ (AB)' = B'A'}

∴ (A²)' = (– A) × (– A) = A × A ......... (from (1))

∴ (A²)' = A²

So, If A is skew symmetric matrix then A² is a symmetric matrix

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