If $$B=52$$α$$1021$$α$$3$$−$$1$$ is the inverse of a $$3$$×$$3$$ matrix A, then the sum of all values of α for which $$det(A)+1=0$$, is

Question

If  $$B=52$$α$$1021$$α$$3$$−$$1$$ is the inverse of a  $$3$$×$$3$$ matrix A, then the sum of all values of α  for which $$det(A)+1=0$$, is

Infinity Learn · Accepted Answer

Given matrix B is the inverse matrix of $$3$$×$$3$$ matrix A,  Where $$B=52$$α$$1021$$α$$3$$−$$1We$$ know that ,$$detA=1detB$$           ∵detA−$$1=1detASince$$, $$det(A)$$ $$+1=01det$$⁡(B)+1=0$$⇒det⁡$$(B)=$$−$$1$$⇒$$5($$−$$2$$−$$3)−$$2$$α$$(0$$−α$$)+1(0$$−$$2$$α$$)=$$−$$1$$⇒−$$25+2$$α$$2$$−$$2$$α$$=$$−$$1$$⇒$$2$$α$$2$$−$$2$$α−$$24=0$$⇒α$$2$$−α−$$12=0$$⇒$$($$α−$$4)($$α$$+3)=0$$⇒α$$=$$−$$3$$,$$4$$ So, required sum of all values of α is $$4$$−$$3=1$$

If $B = [\begin{matrix} 5 & 2 α & 1 \\ 0 & 2 & 1 \\ α & 3 & - 1 \end{matrix}]$ is the inverse of a $3 \times 3$ matrix A, then the sum of all values of $α$ for which det(A)+1=0, is

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If B=52α1021α3−1 is the inverse of a 3×3 matrix A, then the sum of all values of α for which det(A)+1=0, is

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If $B = [\begin{matrix} 5 & 2 α & 1 \\ 0 & 2 & 1 \\ α & 3 & - 1 \end{matrix}]$ is the inverse of a $3 \times 3$ matrix A, then the sum of all values of $α$ for which det(A)+1=0, is