(B) Given $A = \begin{bmatrix} k & 2 \\ 2 & k \end{bmatrix}$.First,calculate the determinant of $A$:$|A| = (k \times k) - (2 \times 2) = k^2 - 4$.We k

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(B) Given $A = \begin{bmatrix} k & 2 \\ 2 & k \end{bmatrix}$.First,calculate the determinant of $A$:$|A| = (k \times k) - (2 \times 2) = k^2 - 4$.We know the property of determinants that $|A^n| = |A|^n$.Given $|A^3| = 125$,we can write this as $|A|^3 = 125$.Substituting the value of $|A|$:$(k^2 - 4)^3 = 125$.Taking the cube root on both sides:$k^2 - 4 = 5$.$k^2 = 9$.$k = \pm 3$.

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 $A = \begin{bmatrix} k & 2 \\ 2 & k \end{bmatrix}$ and $|A^3| = 125$,then the value of $k$ is

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$\pm 2$
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$\pm 3$
C
$-5$
D
$-4$

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3 and 4 .Determinants and Matrices

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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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