If A is a skew symmetric matrix, then \( A^2 \) is a
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → symmetric matrix
Since A is skew symmetric, \( A'=-A \). Using \( (AB)'=B'A' \):
\( \displaystyle (A^2)'=(AA)'=A'A' \)
\( \displaystyle =(-A)(-A)=A^2 \)
Since \( (A^2)'=A^2 \), \( A^2 \) is a symmetric matrix.
It need not be the zero or the identity matrix: for \( A=\begin{bmatrix}0 & 1\\-1 & 0\end{bmatrix} \), \( A^2=-I \).
Tip: Every even power of a skew symmetric matrix is symmetric, and every odd power is skew symmetric.
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Matrices
