AIEEE 2007 | Matrices and Determinants Question 293 | Mathematics

Let $$A = \left| {\matrix{ 5 & {5\alpha } & \alpha \cr 0 & \alpha & {5\alpha } \cr 0 & 0 & 5 \cr } } \right|.$$ If $$\,\,\left| {{A^2}} \right| = 25,$$ then $$\,\left| \alpha \right|$$ equals

$$1/5$$

$$5$$

$${5^2}$$

$$1$$

AIEEE 2007

MCQ (Single Correct Answer)

-1

If $$D = \left| {\matrix{ 1 & 1 & 1 \cr 1 & {1 + x} & 1 \cr 1 & 1 & {1 + y} \cr } } \right|$$ for $$x \ne 0,y \ne 0,$$ then $$D$$ is :

divisible by $$x$$ but not $$y$$

divisible by $$y$$ but not $$x$$

divisible by neither $$x$$ nor $$y$$

divisible by both $$x$$ and $$y$$

AIEEE 2006

MCQ (Single Correct Answer)

-1

If $$A$$ and $$B$$ are square matrices of size $$n\, \times \,n$$ such that
$${A^2} - {B^2} = \left( {A - B} \right)\left( {A + B} \right),$$ then which of the following will be always true?

$$A=B$$

$$AB=BA$$

either of $$A$$ or $$B$$ is a zero matrix

either of $$A$$ or $$B$$ is identity matrix

AIEEE 2006

MCQ (Single Correct Answer)

-1

Let $$A = \left( {\matrix{ 1 & 2 \cr 3 & 4 \cr } } \right)$$ and $$B = \left( {\matrix{ a & 0 \cr 0 & b \cr } } \right),a,b \in N.$$ Then

there cannot exist any $$B$$ such that $$AB=BA$$

there exist more then one but finite number of $$B'$$s such that $$AB=BA$$

there exists exactly one $$B$$ such that $$AB=BA$$

there exist infinitely many $$B'$$s such that $$AB=BA$$