If $A=\begin{pmatrix} -a & b\\c & a\end{pmatrix}$ and $A^2=I$, where $I$ is an Identity matrix of order 2, then which of the following is correct ?
Answer & explanation
Correct answer: option 4
$A=\begin{bmatrix} -a & b\\c & a\end{bmatrix}$ and $A^2=I$
$A×A=\begin{bmatrix} -a & b\\c & a\end{bmatrix}\begin{bmatrix} -a & b\\c & a\end{bmatrix}=\begin{bmatrix}a^2+bc & 0\\0 & a^2+bc\end{bmatrix}=I=\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$
so $1-bc-a^2=0$ (on comparison)