1
MHT CET 2022 11th August Evening Shift
+2
-0

If $$A=\left[\begin{array}{lll}1 & 2 & 1 \\ 3 & 1 & 3\end{array}\right]$$ and $$B=\left[\begin{array}{ll}2 & 3 \\ 1 & 2 \\ 1 & 2\end{array}\right]$$, then $$(A B)^{-1}=$$

A
$$\left[\begin{array}{ll}\frac{17}{5} & \frac{9}{5} \\ 2 & 1\end{array}\right]$$
B
$$\left[\begin{array}{cc}\frac{-17}{5} & \frac{9}{5} \\ 2 & -1\end{array}\right]$$
C
$$\left[\begin{array}{ll}\frac{17}{5} & 2 \\ \frac{9}{5} & 1\end{array}\right]$$
D
$$\left[\begin{array}{cc}\frac{-17}{5} & 2 \\ \frac{-9}{5} & -1\end{array}\right]$$
2
MHT CET 2022 11th August Evening Shift
+2
-0

Given $$A=\left[\begin{array}{ccc}x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z\end{array}\right]$$, if $$x y z=60$$ and $$8 x+4 y+3 z=20$$, then $$A$$.(adjA)

A
$$\left[\begin{array}{ccc}60 & 0 & 0 \\ 0 & 60 & 0 \\ 0 & 0 & 60\end{array}\right]$$
B
$$\left[\begin{array}{ccc}108 & 0 & 0 \\ 0 & 108 & 0 \\ 0 & 0 & 108\end{array}\right]$$
C
$$\left[\begin{array}{ccc}20 & 0 & 0 \\ 0 & 20 & 0 \\ 0 & 0 & 20\end{array}\right]$$
D
$$\left[\begin{array}{ccc}68 & 0 & 0 \\ 0 & 68 & 0 \\ 0 & 0 & 68\end{array}\right]$$
3
MHT CET 2021 24th September Evening Shift
+2
-0

If $$\mathrm{A}=\left[\begin{array}{cc}\lambda & \mathrm{i} \\ \mathrm{i} & -\lambda\end{array}\right]$$ and $$\mathrm{A}^{-1}$$ does not exist, then $$\lambda=$$ (where $$\mathrm{i}=\sqrt{-1}$$)

A
$$\pm 2$$
B
$$\pm 1$$
C
0
D
$$\pm 3$$
4
MHT CET 2021 24th September Evening Shift
+2
-0

If $$A=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$$, and $$A(\operatorname{adj} A)=k I$$, then the value of $$(k+1)^4$$ is

A
256
B
81
C
16
D
625
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