Let $A=\left[a_{i j} ight]_{2 imes 2}$, where $a_{i j}
eq 0$ for all $i, j$ and $A^2=I$. Let $a

Question

Let $A=\left[a_{i j}ight]_{2 	imes 2}$, where $a_{i j} 
eq 0$ for all $i, j$ and $A^2=I$. Let $a$ be the sum of all diagonal elements of $A$ and $b=|A|$. Then, $4 a^2+3 b^2$ is equal to

Professor PC Thomas Classes · Answer

Cayley-Hamilton theorem determines $4a^2+3b^2 = 3$.