Practicing Success
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 ? |
$1+2b-c^2=0$ $1+b^2-ac=0$ $1+bc-a^2=0$ $1-bc-a^2=0$ |
$1-bc-a^2=0$ |
$A=\begin{bmatrix} -a & b\\c & a\end{bmatrix}$ 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) |