1. Tardigrade
  2. Question
  3. Mathematics
  4. If A is a matrix [ 1 -1 0 0 2 a 1 1 2 ] , then the number of real value (.s.) of 'a' for which A(.adjA.)=adj(.adjA.), is (where adjA denotes adjoint of matrix A )

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $A$ is a matrix $\begin{bmatrix} 1 & -1 & 0 \\ 0 & 2 & a \\ 1 & 1 & 2 \end{bmatrix}$ , then the number of real value $\left(\right.s\left.\right)$ of $'a'$ for which $A\left(\right.adjA\left.\right)=adj\left(\right.adjA\left.\right),$ is (where $adjA$ denotes adjoint of matrix $A$ )

NTA AbhyasNTA Abhyas 2022

Solution:

$\left|\right.A\left|\right.=4-a+1\left(\right.-a\left.\right)=4-2a$
$A\left(\right.AdjA\left.\right)=\left|\right.A\left|\right.I=\left(\right.4-2a\left.\right)I$
$Adj\left(\right.AdjA\left.\right)=\left|\right.A\left|\right.A=\left(\right.4-2a\left.\right)A$
$\left(\right.4-2a\left.\right)I=\left(\right.4-2a\left.\right)A$
$\Rightarrow \left(\right.4-2a\left.\right)\left(\right.A-I\left.\right)=0\Rightarrow a=2$