If A=pmatrix0&-11&0pmatrix, then which one of the following statements is NOT correct?

Question

If $A=\begin{pmatrix}0&-1\1&0\end{pmatrix}$, then which one of the following statements is NOT correct?

Accepted Answer

$A^2=-I$, $A^3=\begin{pmatrix}0&1\-1&0\end{pmatrix}$, $A^4=I$.

Checking (A): $A^2+I=O$, while $A(A^2-I)=A(-2I)=-2A
e O$ in general --- so (A) is false (the statement that is NOT correct).

(The others check out with direct substitution using $A^2=-I,\ A^4=I$.)

Solutions · 1