If A is a square matrix of order 3 and |A|=5, | vedclass

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

Question

(B) We know that for a square matrix $A$ of order $n$,the property of the adjoint matrix is given by $A 	ext{ adj. } A = |A| I$,where $I$ is the iden

Vedclass · Accepted Answer

$125$

Vedclass · Answer

(B) We know that for a square matrix $A$ of order $n$,the property of the adjoint matrix is given by $A 	ext{ adj. } A = |A| I$,where $I$ is the identity matrix of order $n$. Taking the determinant on both sides,we get $|A 	ext{ adj. } A| = | |A| I |$. Since $|kI| = k^n |I|$ for a matrix of order $n$,we have $|A 	ext{ adj. } A| = |A|^n |I|$. Since $|I| = 1$,the formula becomes $|A 	ext{ adj. } A| = |A|^n$. Given that $n = 3$ and $|A| = 5$,we substitute these values into the formula: $|A 	ext{ adj. } A| = (5)^3 = 125$.

If $A$ is a square matrix of order $3$ and $|A|=5$,then $|A \text{ adj. } A|$ is

Similar Questions

If matrix $A=\begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix}$ is such that $AX=I$,where $I$ is a $2 \times 2$ unit matrix,then $X=$

If matrix $A = \begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix}$ such that $AX = I$,then $X = \dots$

The inverse of matrix $A = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ is

Let $A=\left[\begin{array}{ccc}1 & -2 & 1 \\ -2 & 3 & 1 \\ 1 & 1 & 5\end{array}\right]$. Verify that $\left(A^{-1}\right)^{-1}=A$.

If $A = \begin{bmatrix} \sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha \end{bmatrix}$ and $A + A^{-1} = I$,then $\alpha =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module