1
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$A=\left[\begin{array}{ll}2 & 2 \\ 3 & 4\end{array}\right]$$, then $$A^{-1}$$ equals to

A
$$\left[\begin{array}{cc}2 & 1 \\ -3 / 2 & -1\end{array}\right]$$
B
$$\left[\begin{array}{cc}2 & -1 \\ -3 / 2 & 1\end{array}\right]$$
C
$$\left[\begin{array}{cc}-2 & 1 \\ 3 / 2 & -1\end{array}\right]$$
D
$$\left[\begin{array}{cc}-2 & -1 \\ 3 / 2 & 1\end{array}\right]$$
2
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$A$$ is a matrix of order $$4 \operatorname{such}$$ that $$A(\operatorname{adj} A)=10 \mathrm{~I}$$, then $$|\operatorname{adj} A|$$ is equal to

A
10
B
100
C
1000
D
10000
3
COMEDK 2023 Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $$A=\left[\begin{array}{cc}k+1 & 2 \\ 4 & k-1\end{array}\right]$$ is a singular matrix, then possible values of $$\mathrm{k}$$ are

A
$$\pm 1$$
B
$$\pm 2$$
C
$$\pm 3$$
D
$$\pm 4$$
4
COMEDK 2023 Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \text { If } A=\left(\begin{array}{ll} 1 & 2 \\ 0 & 1 \end{array}\right) \quad P=\left(\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right) \quad Q=P^T A P, \quad \text { then } P Q^{2014} P^T \text { is equal to } $$

A
$$ \left(\begin{array}{cc} 1 & 2^{2014} \\ 0 & 1 \end{array}\right) $$
B
$$ \left(\begin{array}{cc} 1 & 4028 \\ 0 & 1 \end{array}\right) $$
C
$$ \left(P^T\right)^{2013} A^{2014} P^{2013} $$
D
$$ P^T A^{2014} P $$
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