MAT1503-Exam OCt/Nov 2024 Assume that $$ A $$ is a $$ 2 imes 2 $$ matrix with integer entries. If $$ B $$ is the inverse of $$ A $$ and $$ B $$ has integer entries, then choose the correct statement: $$ \operatorname{det}(A)= \pm 1 $$ and $$ \operatorname{det}(B)= \pm 1 $$ $$ \operatorname{det}(A)=-1 $$ or $$ \operatorname{det}(A)=0 $$ $$ \operatorname{det}(A)=1 $$ or $$ \operatorname{det}(A)=0 $$ and $$ B $$ has integer $$ \operatorname{entries} $$ None of the given options det $$ (A)=-1 $$ and $$ \operatorname{det}(A)=0 $$

Question

MAT1503-Exam OCt/Nov 2024 Assume that $$ A $$ is a $$ 2 	imes 2 $$ matrix with integer entries. If $$ B $$ is the inverse of $$ A $$ and $$ B $$ has integer entries, then choose the correct statement: $$ \operatorname{det}(A)= \pm 1 $$ and $$ \operatorname{det}(B)= \pm 1 $$ $$ \operatorname{det}(A)=-1 $$ or $$ \operatorname{det}(A)=0 $$ $$ \operatorname{det}(A)=1 $$ or $$ \operatorname{det}(A)=0 $$ and $$ B $$ has integer $$ \operatorname{entries} $$ None of the given options det $$ (A)=-1 $$ and $$ \operatorname{det}(A)=0 $$

Young Tyler · Accepted Answer

The correct statement is $$ \operatorname{det}(A)= \pm 1 $$ and $$ \operatorname{det}(B)= \pm 1 $$.

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