JEE Main 2022 · 26 Jul · Shift 2, Mathematics question 30

$A^2=I$. Either $A=\pm I$ (2 matrices), or $a+d=0$ and $a^2+bc=1$.

$d=-a$ keeps both in $\{-1,\dots,10\}$ only for $a\in\{-1,0,1\}$.

• $a=0$: $bc=1$, 2 ways.
• $a=\pm1$: $bc=0$, $12+12-1=23$ ways each.

Total $2+2+46=50$.

Answer: 50