JEE Main 2021 (Online) 26th February Morning ShiftQuestion 1
Let $A$ be a symmetric matrix of order $2$ with integer entries. If the sum of the diagonal elements of $A^{2}$ is $1$, then the possible number of such matrices is :
Matrices
Solution
$A=\begin{bmatrix}a&b\\b&c\end{bmatrix}$, $\operatorname{tr}(A^2)=a^2+2b^2+c^2=1$. $b\neq0$ gives $\ge2$, so $b=0$ and $a^2+c^2=1$: $(a,c)=(\pm1,0),(0,\pm1)$, i.e. $4$ matrices. Option (B).