1
AIEEE 2007
+4
-1
Out of Syllabus
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
A
$$1/5$$
B
$$5$$
C
$${5^2}$$
D
$$1$$
2
AIEEE 2006
+4
-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
$$A=B$$
B
$$AB=BA$$
C
either of $$A$$ or $$B$$ is a zero matrix
D
either of $$A$$ or $$B$$ is identity matrix
3
AIEEE 2006
+4
-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
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 $$AB=BA$$
4
AIEEE 2005
+4
-1
If $${A^2} - A + 1 = 0$$, then the inverse of $$A$$ is :
A
$$A+I$$
B
$$A$$
C
$$A-I$$
D
$$I-A$$
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