(B) First,we calculate the determinant of matrix $A$:$|A| = 1(1 \times 1 - 2 \times 1) - 3(2 \times 1 - 2 \times 5) + 4(2 \times 1 - 1 \times 5)$$|A|

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(B) First,we calculate the determinant of matrix $A$:$|A| = 1(1 \times 1 - 2 \times 1) - 3(2 \times 1 - 2 \times 5) + 4(2 \times 1 - 1 \times 5)$$|A| = 1(1 - 2) - 3(2 - 10) + 4(2 - 5)$$|A| = 1(-1) - 3(-8) + 4(-3)$$|A| = -1 + 24 - 12 = 11$We know the property $|\text{adj } A| = |A|^{n-1}$,where $n$ is the order of the matrix.Here,$n = 3$,so $|\text{adj } A| = |A|^{3-1} = |A|^2$.$|\text{adj } A| = (11)^2 = 121$.

Class 12 Mathematics 3-4. Matrices and Determinants Adjoint and inverse of matrices

Easy

If $A = \begin{bmatrix} 1 & 3 & 4 \\ 2 & 1 & 2 \\ 5 & 1 & 1 \end{bmatrix}$,then $|\text{adj } A| = $ . . . . . .

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A
$1331$
B
$121$
C
$11$
D
$1$

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3-4. Matrices and Determinants

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Adjoint and inverse of matrices

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If $A = \begin{bmatrix} 1 & 3 & 4 \\ 2 & 1 & 2 \\ 5 & 1 & 1 \end{bmatrix}$,then $|\text{adj } A| = $ . . . . . .

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If $x, y, z$ are nonzero real numbers,then the inverse of matrix $A = \begin{bmatrix} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \end{bmatrix}$ is

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