33
MCQ (Single Correct Answer)
If $A=\left|\begin{array}{rrr}2 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3\end{array}\right|$, then $A^{-1}$ exists, if
A
$\lambda=2$
B
$\lambda \neq 2$
C
$\lambda \neq-2$
D
None of these
34
MCQ (Single Correct Answer)
If $A$ and $B$ are invertible matrices, then which of the following is not correct?
A
$\operatorname{adj} A=|A| \cdot A^{-1}$
B
$\operatorname{det}(A)^{-1}=[\operatorname{det}(A)]^{-1}$
C
$(A B)^{-1}=B^{-1} A^{-1}$
D
$(A+B)^{-1}=B^{-1}+A^{-1}$
35
MCQ (Single Correct Answer)
If $x, y$ and $z$ are all different from zero and $\left|\begin{array}{ccc}1+x & 1 & 1 \\ 1 & 1+y & 1 \\ 1 & 1 & 1+z\end{array}\right|=0$, then the value of $x^{-1}+y^{-1}+z^{-1}$ is
A
$x y z$
B
$x^{-1} y^{-1} z^{-1}$
C
$-x-y-z$
D
$-1$
36
MCQ (Single Correct Answer)
The value of $\left|\begin{array}{ccc}x & x+y & x+2 y \\ x+2 y & x & x+y \\ x+y & x+2 y & x\end{array}\right|$ is
A
$9 x^2(x+y)$
B
$9 y^2(x+y)$
C
$3 y^2(x+y)$
D
$7 x^2(x+y)$
37
If $A$ is a matrix of order $3 \times 3$, then $|3 A|$ is equal to ............. .
Explanation
If $A$ is a matrix of order $3 \times 3$, then $|3 A|=3 \times 3 \times 3|A|=27|A|$