(B) Given,$A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$.The determinant of matrix $A$ is denoted by $|A|$ or $\det(A)$.$|A| = (a \times d) - (b \

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(B) Given,$A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$.The determinant of matrix $A$ is denoted by $|A|$ or $\det(A)$.$|A| = (a \times d) - (b \times c) = ad - bc$.The expression $|A|^{-1}$ represents the multiplicative inverse of the determinant value $|A|$.Therefore,$|A|^{-1} = \frac{1}{|A|} = \frac{1}{ad - bc}$.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

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If matrix $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$,then $|A|^{-1}$ is equal to

MHT CET 2010 All MHT CET

A
$ad - bc$
B
$\frac{1}{ad - bc}$
C
$\frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}$
D
None of these

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Expansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line

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MediumAP EAMCET 2002

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EasyMHT CET 2011

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DifficultAP EAMCET 2021

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If matrix $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$,then $|A|^{-1}$ is equal to

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The value of $a$ for which the system of equations has a non-zero solution is
$a^{3} x+(a+1)^{3} y+(a+2)^{3} z=0$
$a x+(a+1) y+(a+2) z=0$
$x+y+z=0$