The matrix \( P = \begin{bmatrix} 0 & 0 & 4 \\ 0 & 4 & 0 \\ 4 & 0 & 0 \end{bmatrix} \) is a
square matrix
diagonal matrix
unit matrix
none
Total number of possible matrices of order \( 3 \times 3 \) with each entry 2 or 0 is
9
27
81
512
If \( \begin{bmatrix} 2x + y & 4x \\ 5x - 7 & 4x \end{bmatrix} = \begin{bmatrix} 7 & 7y - 13 \\ y & x + 6 \end{bmatrix} \), then the value of \( x + y \) is
x = 3, y = 1
x = 2, y = 3
x = 2, y = 4
x = 3, y = 3
If
\( A = \dfrac{1}{\pi} \begin{bmatrix} \sin^{-1}(x \pi) & \tan^{-1}\left(\dfrac{x}{\pi}\right) \\ \sin^{-1}\left(\dfrac{x}{\pi}\right) & \cot^{-1}(x \pi) \end{bmatrix}, \quad B = \dfrac{1}{\pi} \begin{bmatrix} -\cos^{-1}(x \pi) & \tan^{-1}\left(\dfrac{x}{\pi}\right) \\ \sin^{-1}\left(\dfrac{x}{\pi}\right) & -\tan^{-1}(x \pi) \end{bmatrix} \)
then \( A - B \) is equal to
I
O
2I
\( \dfrac{1}{2} I \)
If A and B are two matrices of the order \( 3 \times m \) and \( 3 \times n \), respectively, and \( m = n \), then the order of matrix \( 5A - 2B \) is
m × 3
3 × 3
m × n
3 × n
If \( A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \), then \( A^2 \) is equal to
\( \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \)
\( \begin{bmatrix} 1 & 0 \\ 1 & 0 \end{bmatrix} \)
\( \begin{bmatrix} 0 & 1 \\ 0 & 1 \end{bmatrix} \)
\( \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \)
If matrix \( A = [a_{ij}]_{2 \times 2} \), where \( a_{ij} = 1 \) if \( i \neq j \) and \( a_{ij} = 0 \) if \( i = j \), then \( A^2 \) is equal to
I
A
0
None of these
The matrix \( \begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4 \end{bmatrix} \) is a
identity matrix
symmetric matrix
skew symmetric matrix
none of these
The matrix \( \begin{bmatrix} 0 & -5 & 8 \\ 5 & 0 & 12 \\ -8 & -12 & 0 \end{bmatrix} \) is a
diagonal matrix
symmetric matrix
skew symmetric matrix
scalar matrix
If A is a matrix of order m × n and B is a matrix such that AB' and B'A are both defined, then order of matrix B is
m × m
n × n
n × m
m × n
If A and B are matrices of same order, then (AB' − BA') is a
skew symmetric matrix
null matrix
symmetric matrix
unit matrix
If A is a square matrix such that \( A^2 = I \), then \( (A^{-1})^3 + (A + I)^3 - 7A \) is equal to
A
I − A
I + A
3A
For any two matrices A and B, we have
AB = BA
AB ≠ BA
AB = O
None of the above
On using elementary column operations \( C_2 \rightarrow C_2 - 2C_1 \) in the following matrix equation
\( \begin{bmatrix} 1 & -3 \\ 2 & 4 \end{bmatrix} = \begin{bmatrix} 1 & -1 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} 3 & 1 \\ 2 & 4 \end{bmatrix} \), we have:
\( \begin{bmatrix} 1 & -5 \\ 0 & 4 \end{bmatrix} = \begin{bmatrix} 1 & -1 \\ -2 & 2 \end{bmatrix} \begin{bmatrix} 3 & -5 \\ 2 & 0 \end{bmatrix} \)
\( \begin{bmatrix} 1 & -5 \\ 0 & 4 \end{bmatrix} = \begin{bmatrix} 1 & -1 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} 3 & -5 \\ -0 & 2 \end{bmatrix} \)
\( \begin{bmatrix} 1 & -5 \\ 2 & 0 \end{bmatrix} = \begin{bmatrix} 1 & -3 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} 3 & 1 \\ -2 & 4 \end{bmatrix} \)
\( \begin{bmatrix} 1 & -5 \\ 2 & 0 \end{bmatrix} = \begin{bmatrix} 1 & -1 \\ -3 & -3 \\ \end{bmatrix} \begin{bmatrix} 3 & -5 \\ 2 & 0 \end{bmatrix} \)
On using elementary row operation \( R_1 \rightarrow R_1 - 3R_2 \) in the following matrix equation:
\( \begin{bmatrix} 4 & 2 \\ 3 & 3 \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix} \begin{bmatrix} 2 & 0 \\ 1 & 1 \end{bmatrix} \), we have:
\( \begin{bmatrix} -5 & -7 \\ 3 & 3 \end{bmatrix} = \begin{bmatrix} 1 & -7 \\ 0 & 3 \end{bmatrix} \begin{bmatrix} 2 & 0 \\ 1 & 1 \end{bmatrix} \)
\( \begin{bmatrix} -5 & -7 \\ 3 & 3 \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix} \begin{bmatrix} -1 & -3 \\ 1 & 1 \end{bmatrix} \)
\( \begin{bmatrix} -5 & -7 \\ 3 & 3 \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ 1 & -7 \end{bmatrix} \begin{bmatrix} 2 & 0 \\ 1 & 1 \end{bmatrix} \)
\( \begin{bmatrix} 4 & 2 \\ -5 & -7 \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ -3 & -3 \end{bmatrix} \begin{bmatrix} 2 & 0 \\ 1 & 1 \end{bmatrix} \)