Question

if an idempotent matrix is also skew symmetric then it must be

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

Answer 1

Answer: (D)

a null matrix

$f\left(A\right)=A^2-A$

$f(-A)=(-A{)}^2+A$

$=(A^2+A)=-[A^2-A]$

$A^2+A=-A^2+A$

$A^2=0$