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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 $|3 A|=3 \times 3 \times 3|A|=27|A|$

38

If $A$ is invertible matrix of order $3 \times 3$, then $\left|A^{-1}\right|$ is equal to ............. .

Explanation

If $A$ is invertible matrix of order $3 \times 3$, then $\left|A^{-1}\right|=\frac{1}{|A|}$. $\left[\right.$ since, $\left.|A| \cdot\left|A^{-1}\right|=1\right]$