Let A = ( ll 2 & -2 1 & -1 ) and B = ( ll -1 & 2 -1 & 2 ). Then t… - Vidyadip

Question

Let $A =\left(\begin{array}{ll}2 & -2 \\ 1 & -1\end{array}\right)$ and $B =\left(\begin{array}{ll}-1 & 2 \\ -1 & 2\end{array}\right)$. Then the number of elements in the set $\left\{( n , m ): n , m \in\{1,2, \ldots . .10\}\right.$ and $\left.nA ^{ n }+ mB ^{ m }= I \right\}$ is

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Answer

a
$A ^{2}= A$ and $B ^{2}= B$

Therefore equation $nA ^{ n }+ mB ^{ m }= I$ becomes $nA + mB = I$, which gives $m = n =1$

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