New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Matrices and Determinants question

2006 · Shift 0 · Q60

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Matrices and Determinants
2006 · Shift 0 · Q60

Matrices and Determinants question

2006 · Shift 0 · Q60

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

Let

A = \left( {\begin{matrix} 1 & 2 \\ 3 & 4 \\ \end{matrix} } \right)

and

B = \left( {\begin{matrix} a & 0 \\ 0 & b \\ \end{matrix} } \right),a,b \in N.

Then

A
there cannot exist any $B$ such that $AB=BA$
B
there exist more then one but finite number of $B'$ s such that $AB=BA$
C
there exists exactly one $B$ such that $AB=BA$
D
there exist infinitely many $B'$ s such that $AB=BA$

More from Matrices and Determinants

If $A^{2} - A + 1 = 0$ , then the inverse of $A$ is :2005 · MCQ
The system of equations $α x + y + z = α - 1 x + α y + z = α - 1 x + y + α z = α - 1$ has no solutions, if $α$ is :2005 · MCQ
If $a_{1}, a_{2}, a_{3}, ........, a_{n}, .....$ are in G.P., then the determinant $Δ = lo g a_{n} lo g a_{n + 3} lo g a_{n + 6} lo g a_{n + 1} lo g a_{n + 4} lo g a_{n + 7} lo g a_{n + 2} lo g a_{n + 5} lo g a_{n + 8}$ …2005 · MCQ
If $a^{2} + b^{2} + c^{2} = - 2$ and f $(x) = 1 + a^{2} x (1 + a^{2}) x (1 + a^{2}) x (1 + b^{2}) x 1 + b^{2} x (1 + b^{2}) x (1 + c^{2}) x (1 + c^{2}) x 1 + c^{2} x,$ …2005 · MCQ
Let $A = 121 - 1 11 1 - 3 1 .$ and $10$ $B = 4 - 5 1 20 - 2 2 α 3$ …2004 · MCQ
Let $A = 00 - 1 0 - 1 0 - 1 00$ . The only correct statement about the matrix $A$ is2004 · MCQ
If $a_{1}, a_{2}, a_{3}, ........., a_{n}, ......$ are in G.P., then the value of the determinant $lo g a_{n} lo g a_{n + 3} lo g a_{n + 6} lo g a_{n + 1} lo g a_{n + 4} lo g a_{n + 7} lo g a_{n + 2} lo g a_{n + 5} lo g a_{n + 8},$ …2004 · MCQ
If $A = [a b b a]$ and $A^{2} = [α β β α]$ , then2003 · MCQ