New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Matrices and Determinants question

2011 · Shift 0 · Q42

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

PYQ Library
JEE Main
Mathematics
Matrices and Determinants
2011 · Shift 0 · Q42

Matrices and Determinants question

2011 · Shift 0 · Q42

JEE MainMathematicsMatrices and DeterminantsMCQ+4 / −1

Let

A

and

B

be two symmetric matrices of order

3

. Statement - 1 :

A(BA)

and

(AB)A

are symmetric matrices. Statement - 2 :

AB

is symmetric matrix if matrix multiplication of

A

with

B

is commutative.

A
statement - 1 is true, statement - 2 is true; statement - 2 is not a correct explanation for statement - 1.
B
statement - 1 is true, statement - 2 is false.
C
statement - 1 is false, statement -2 is true
D
statement -1 is true, statement - 2 is true; statement - 2 is a correct explanation for statement - 1.

More from Matrices and Determinants

The number of $3 \times 3$ non-singular matrices, with four entries as $1$ and all other entries as $0$ , is :2010 · MCQ
Consider the system of linear equations; $x_{1} + 2 x_{2} + x_{3} = 3 2 x_{1} + 3 x_{2} + x_{3} = 3 3 x_{1} + 5 x_{2} + 2 x_{3} = 1$ The system has :2010 · MCQ
Let $A$ be a $A^{2} = I,$ matrix with non-zero entries and let $A^{2} = I,$ where $I$ is $2 \times 2$ identity matrix. Define $T r (A) =$ sum of diagonal elements of $A$ and $∣ A ∣ =$ determinant of matrix $A$ . Statement- 1: $T r (A) = 0$ …2010 · MCQ
Let $a, b, c$ be such that $b (a + c) e 0$ if $a - b c a + 1 b + 1 c - 1 a - 1 b - 1 c + 1 + a + 1 a - 1 (- 1)^{n + 2} a b + 1 b - 1 (- 1)^{n + 1} b c - 1 c + 1 (- 1)^{n} c = 0$ …2009 · MCQ
Let $a, b, c$ be any real numbers. Suppose that there are real numbers $x, y, z$ not all zero such that $x = cy + b z, y = a z + c x,$ and $z = b x + a y .$ Then $a^{2} + b^{2} + c^{2} + 2 ab c$ is equal to :2008 · MCQ
Let $A$ be $a 2 \times 2$ matrix with real entries. Let $I$ be the $2 \times 2$ identity matrix. Denote by tr $(A)$ , the sum of diagonal entries of $a$ . Assume that $a^{2} = I .$ Statement-1 : If $A e I$ and $A e - I$ , then det $(A) = - 1$ …2008 · MCQ
If $D = 111 1 1 + x 1 11 1 + y$ for $x e 0, y e 0,$ then $D$ is :2007 · MCQ
If $A$ and $B$ are square matrices of size $n \times n$ such that $A^{2} - B^{2} = (A - B) (A + B),$ then which of the following will be always true?2006 · MCQ