1
WB JEE 2024
MCQ (Single Correct Answer)
+2
-0.5
Change Language

Let $$A=\left[\begin{array}{ccc}0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0\end{array}\right]$$, then

A
$$\mathrm{A}$$ is a null matrix
B
$$\mathrm{A}$$ is skew symmetric matrix
C
$$\mathrm{A}^{-1}$$ does not exist
D
$$\mathrm{A}^2=\mathrm{I}$$
2
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let A and B are orthogonal matrices and det A + det B = 0. Then

A
A + B is singular
B
A + B is non-singular
C
A + B is orthogonal
D
A + B is skew symmetric
3
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let $$A = \left( {\matrix{ 2 & 0 & 3 \cr 4 & 7 & {11} \cr 5 & 4 & 8 \cr } } \right)$$. Then

A
det A is divisible by 11
B
det A is not divisible by 11
C
det A = 0
D
A is orthogonal matrix
4
WB JEE 2023
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If the matrix Mr is given by $${M_r} = \left( {\matrix{ r & {r - 1} \cr {r - 1} & r \cr } } \right)$$ for r = 1, 2, 3, ... then det (M1) + det (M2) + ... + det (M2008) =

A
2007
B
2008
C
(2008)$$^2$$
D
(2007)$$^2$$
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