Question

If an idempotent matrix is also skew symmetrix, then it must be

• A. an involuntary matrix
• B. an identity matrix
• C. an orthogonal matrix
• D. a null matrix

Answer 1

The correct option is D a null matrix

$A^{\prime }=-A$ and $A^2=A$

So $(A^2{)}^{\prime }=A^{\prime }\Rightarrow (A^{\prime }{)}^2=-A$

$\Rightarrow (-A{)}^2=-A\Rightarrow A=-A$

$\Rightarrow A=O$