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If $|\begin{array}{ccc} x^{2} + x & x + 1 & x - 2 \\ 2 x^{2} + 3 x - 1 & 3 x & 3 x - 3 \\ x^{2} + 2 x + 3 & 2 x - 1 & 2 x - 1 \end{array}| = A x + B$ then $A$ is equal to:

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Correct option is C

Applying R2→R2−R1−R3 we get,Ax+B=x2+xx+1x−2−400x2+2x+32x−12x−1Expanding along R2, we getAx+B=(−1)(−4)x+1x−22x−12x−1=43x−202x−1=4(3)(2x−1)=24x−12Thus A = 24

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If x2+xx+1x−22x2+3x−13x3x−3x2+2x+32x−12x−1=Ax+B then A is equal to:

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If $|\begin{array}{ccc} x^{2} + x & x + 1 & x - 2 \\ 2 x^{2} + 3 x - 1 & 3 x & 3 x - 3 \\ x^{2} + 2 x + 3 & 2 x - 1 & 2 x - 1 \end{array}| = A x + B$ then $A$ is equal to: