(A) matrix $A$ is singular if its determinant is zero,i.e.,$|A| = 0$.We know the property of the adjoint of a matrix: $|\text{adj } A| = |A|^{n-1}$,wh

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(A) matrix $A$ is singular if its determinant is zero,i.e.,$|A| = 0$.We know the property of the adjoint of a matrix: $|\text{adj } A| = |A|^{n-1}$,where $n$ is the order of the matrix $A$.If $n > 1$,then since $|A| = 0$,we have $|\text{adj } A| = 0^{n-1} = 0$.Therefore,$\text{adj } A$ is also a singular matrix.

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

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If $A$ is a singular matrix,then $\text{adj } A$ is

A
Singular
B
Non-singular
C
Symmetric
D
Not defined

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3 and 4 .Determinants and Matrices

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Adjoint and inverse of matrices

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If $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 3 \\ 1 & 0 & 1 \end{bmatrix}$,then $|\operatorname{adj} A| = $ . . . . . . .

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If $A$ is a singular matrix,then $\text{adj } A$ is

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If $A = \begin{bmatrix} 1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4 \end{bmatrix}$ and $A(\operatorname{adj} A) = kI$,then the value of $(k+1)^4$ is

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