62
MCQ (Single Correct Answer)
If $A$ is matrix of order $m \times n$ and $B$ is a matrix such that $A B^{\prime}$ and $B^{\prime} A$ are both defined, then order of matrix $B$ is
A
$m \times m$
B
$n \times n$
C
$n \times m$
D
$m \times n$
63
MCQ (Single Correct Answer)
If $A$ and $B$ are matrices of same order, then $\left(A B^{\prime}-B A^{\prime}\right)$ is
A
skew-symmetric matrix
B
null matrix
C
symmetric matrix
D
unit matrix
64
MCQ (Single Correct Answer)
If $A$ is a square matrix such that $A^2=I$, then $(A-I)^3+(A+I)^3-7 A$ is equal to
A
$A$
B
$I-A$
C
$I+A$
D
$3 A$
65
MCQ (Single Correct Answer)
For any two matrices $A$ and $B$, we have
A
$A B=B A$
B
$A B \neq B A$
C
$A B=O$
D
None of these
66
MCQ (Single Correct Answer)
Q. 66 On using elementary column operations $C_2 \rightarrow C_2-2 C_1$ in the following matrix equation $\left[\begin{array}{cc}1 & -3 \\ 2 & 4\end{array}\right]=\left[\begin{array}{cc}1 & -1 \\ 0 & 1\end{array}\right]\left[\begin{array}{ll}3 & 1 \\ 2 & 4\end{array}\right]$, we have
A
$\left[\begin{array}{cc}1 & -5 \\ 0 & 4\end{array}\right]=\left[\begin{array}{cc}1 & -1 \\ -2 & 2\end{array}\right]\left[\begin{array}{cc}3 & -5 \\ 2 & 0\end{array}\right]$
B
$\left[\begin{array}{cc}1 & -5 \\ 0 & 4\end{array}\right]=\left[\begin{array}{cc}1 & -1 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}3 & -5 \\ -0 & 2\end{array}\right]$
C
$\left[\begin{array}{cc}1 & -5 \\ 2 & 0\end{array}\right]=\left[\begin{array}{cc}1 & -3 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}3 & 1 \\ -2 & 4\end{array}\right]$
D
$\left[\begin{array}{cc}1 & -5 \\ 2 & 0\end{array}\right]=\left[\begin{array}{cc}1 & -1 \\ 0 & 1\end{array}\right]\left[\begin{array}{cc}3 & -5 \\ 2 & 0\end{array}\right]$