Let A be a nonsingular square matrix of order | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) We know that for any square matrix $A$ of order $n$,the property of the adjoint matrix is given by: $A(adj\, A) = (adj\, A)A = |A|I_n$ Taking the

Vedclass · Accepted Answer

$|A|^{2}$

Vedclass · Answer

(C) We know that for any square matrix $A$ of order $n$,the property of the adjoint matrix is given by: $A(adj\, A) = (adj\, A)A = |A|I_n$ Taking the determinant on both sides: $|A(adj\, A)| = ||A|I_n|$ $|A| \cdot |adj\, A| = |A|^n \cdot |I_n|$ Since $|I_n| = 1$,we have: $|A| \cdot |adj\, A| = |A|^n$ $|adj\, A| = |A|^{n-1}$ Given that the order of the matrix $A$ is $3 	imes 3$,so $n = 3$. Therefore,$|adj\, A| = |A|^{3-1} = |A|^2$. Hence,the correct answer is $C$.

Let $A$ be a nonsingular square matrix of order $3 \times 3$. Then $|adj\, A|$ is equal to

Similar Questions

If $A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} 1/2 & -1/2 & 1/2 \\ -4 & 3 & c \\ 5/2 & -3/2 & 1/2 \end{bmatrix}$,then:

If $\begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} A \begin{bmatrix} -3 & 2 \\ 5 & -3 \end{bmatrix} = I_2$,then $A =$

If $Q$ is the inverse of $A$,where $A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}$ and $10Q = \begin{bmatrix} 4 & 2 & 2 \\ -5 & 0 & x \\ 1 & -2 & 3 \end{bmatrix}$,find $x$.

Find the inverse of the matrix (if it exists): $\left[\begin{array}{lll}1 & 2 & 3 \\ 0 & 2 & 4 \\ 0 & 0 & 5\end{array}\right]$

For two invertible matrices $A$ and $B$ of suitable orders,the value of $(AB)^{-1}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module