1
MHT CET 2023 11th May Evening Shift
+2
-0

If $$\mathrm{A}=\left[\begin{array}{ll}\mathrm{i} & 1 \\ 1 & 0\end{array}\right]$$ where $$\mathrm{i}=\sqrt{-1}$$ and $$\mathrm{B}=\mathrm{A}^{2029}$$, then $$\mathrm{B}^{-1}=$$

A
$$-\mathrm{A}$$
B
$$\operatorname{adj} \mathrm{A}$$
C
$$\mathrm{-I}$$
D
$$-\operatorname{adj} \mathrm{A}$$
2
MHT CET 2023 11th May Morning Shift
+2
-0

If $$P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$$ is the adjoint of a $$3 \times 3$$ matrix $$A$$ and $$|A|=4$$, then value of $$\alpha$$ is

A
4
B
11
C
5
D
0
3
MHT CET 2023 11th May Morning Shift
+2
-0

Let $$\omega \neq 1$$ be a cube root of unity and $$S$$ be the set of all non-singular matrices of the form $$\left[\begin{array}{ccc}1 & a & b \\ \omega & 1 & c \\ \omega^2 & \omega & 1\end{array}\right]$$ where each of $$a, b$$ and $$c$$ is either $$\omega$$ or $$\omega^2$$, then the number of distinct matrices in the set $$\mathrm{S}$$ is

A
2
B
6
C
4
D
8
4
MHT CET 2023 10th May Evening Shift
+2
-0

If $$B=\left[\begin{array}{ccc}3 & \alpha & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3\end{array}\right]$$ is the adjoint of a $$3 \times 3$$ matrix $$\mathrm{A}$$ and $$|\mathrm{A}|=4$$, then $$\alpha$$ is equal to

A
1
B
0
C
$$-$$1
D
$$-$$2
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