1
KCET 2025
MCQ (Single Correct Answer)
+1
-0
If a matrix $A=\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]$ satisfies $A^6=k A^{\prime}$, then the value of $k$ is
A
32
B
1
C
$\frac{1}{32}$
D
6
2
KCET 2025
MCQ (Single Correct Answer)
+1
-0

If $A=\left[\begin{array}{ll}k & 2 \\ 2 & k\end{array}\right]$ and $\left|A^3\right|=125$, then the value of $k$ is

A
$\pm 2$
B
$\pm 3$
C
-5
D
-4
3
KCET 2025
MCQ (Single Correct Answer)
+1
-0

If $A$ is a square matrix satisfying the equation $A^2-5 A+7 I=0$, where $I$ is the $I$ dentity matrix and 0 is null matrix of same order, then $A^{-1}=$

A
$\frac{1}{7}(5 \mathrm{I}-\mathrm{A})$
B
$\frac{1}{7}(\mathrm{~A}-5 \mathrm{I})$
C
$7(5 \mathrm{I}-\mathrm{A})$
D
$\frac{1}{5}(7 \mathrm{I}-\mathrm{A})$
4
KCET 2025
MCQ (Single Correct Answer)
+1
-0
If $A$ is a square matrix of order $3 \times 3, \operatorname{det} A=3$, then the value of $\operatorname{det}\left(3 A^{-1}\right)$ is
A
$\frac{1}{3}$
B
3
C
27
D
9
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