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56
MCQ (Single Correct Answer)

If $A=\frac{1}{\pi}\left[\begin{array}{cc}\sin ^{-1}(x \pi) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & \cot ^{-1}(\pi x)\end{array}\right]$ and $B=\frac{1}{\pi}\left[\begin{array}{cc}-\cos ^{-1}(x \pi) & \tan ^{-1}\left(\frac{x}{\pi}\right) \\ \sin ^{-1}\left(\frac{x}{\pi}\right) & -\tan ^{-1}(\pi x)\end{array}\right]$, then $A-B$ is equal to

A
$I$
B
0
C
$2 I$
D
$\frac{1}{2} I$
57
MCQ (Single Correct Answer)

If $A$ and $B$ are two matrices of the order $3 \times \mathrm{m}$ and $3 \times n$, respectively and $m=n$, then order of matrix $(5 A-2 B)$ is

A
$m \times 3$
B
$3 \times 3$
C
$m \times n$
D
$3 \times n$
58
MCQ (Single Correct Answer)

If $A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$, then $A^2$ is equal to

A
$\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$
B
$\left[\begin{array}{ll}1 & 0 \\ 1 & 0\end{array}\right]$
C
$\left[\begin{array}{ll}0 & 1 \\ 0 & 1\end{array}\right]$
D
$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
59
MCQ (Single Correct Answer)

If matrix $A=\left[a_{i j}\right]_{2 \times 2}$, where $a_{i j}=1$, if $i \neq j=0$ and if $i=j$, then $A^2$ is equal to

A
$I$
B
$A$
C
0
D
None of these
60
MCQ (Single Correct Answer)

The matrix $\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{array}\right]$ is a

A
identity matrix
B
symmetric matrix
C
skew-symmetric matrix
D
None of these