Let A and B be any two n × n matrices such that the following condi

1.	Let A and B be any two n × n matrices such that the following conditions hold : AB = BA and there exist positive integers k and l such that Ak = I (the identity matrix) and Bl = 0 (the zero matrix). Then- (A) A + B = I (B) det (AB) = 0 (C) det (A + B) ≠ 0 (D) (A + B)m = 0 for some integer m
Answer» Correct Option :- (B) det (AB) = 0 Explanation :- A^k = I, B^l = 0 (det (B) = 0) ⇒ det (AB) = 0

Let A and B be any two n × n matrices such that the following conditions hold : AB = BA and there exist positive integers k and l such that Ak = I (the identity matrix) and Bl = 0 (the zero matrix). Then- (A) A + B = I (B) det (AB) = 0 (C) det (A + B) ≠ 0 (D) (A + B)m = 0 for some integer m

Answer»

Correct Option :- (B) det (AB) = 0

Explanation :-

A^k = I, B^l = 0 (det (B) = 0)

⇒ det (AB) = 0

Discussion

No Comment Found

Related InterviewSolutions

When light shines on a p-n junction diode, the current (I) vs, voltage (V) is observed as in the figure below : In which quadrant(s) does the diode generate power, so that it can be used as a solar cell ?A. Quad 1 onlyB. Quad 1 and 3 onlyC. Quad 4 onlyD. Quad 1 and 4 only
The acidity of compounds I-IV in water I. Ethanol II. Acetic Acid III. Phenol IV. Acetonitrile follows the orderA. `IVltIltIIIltII`B. `IltIIltIIIltIV`C. `IVltIltIIltIII`D. `IVltIIIltIltII`
Which of the following results from conjugation in Paramecium ?A. Cell deathB. Cell divisionC. BuddingD. Recombination
Forelimbs if whales, bats, humans and cheetah are examples of which of the following processes?A. Divergent evolutionB. Convergent evolutionC. AdaptationD. Saltation
Let f : R → R be a continuous function satisfying f(x) = x + ∫ f(t) dt ,x∈ [0,x] for all x ∈ R. Then the number of elements in the set S = {x ∈ R ; f(x) = 0} is- (A) 1 (B) 2 (C) 3 (D) 4
Suppose `A=[{:(a,b),(c,d):}]` is real matrix with nonzero entries, ad-bc=0 , and `A^(2)`=A. Then a+d equalsA. 1B. 2C. 3D. 4
In a Mathematics test, the average marks of boys is `x%` and the average marks of girls is `y%` with `xney.` If the average marks of all students is `z%` the ration of the number of girls to the total number of students isA. `(z-x)/(y-x)`B. `(z-y)/(y-x)`C. `(z+y)/(y-x)`D. `(z+x)/(y-x)`
Let S be the set of all points `((a)/(b),(c)/(d))` on the circle with radius 1 centred at (0,0) where a and b are relatively prime integers, c and d are relatively prime integers (that is HCF (a, b) = HCF (c,d) = 1), and the integers b and d are even. Then the set SA. is emptyB. has four elementsC. has eight elementsD. is infinite
On a horizontal frictionless frozen lake, a girl (36 kg) and a box (9 kg) are connected to each other by means of a rope. Initially they are 20 m apart. The girl exerts a horizontal force on the box, pulling it towards her. How far has the girl traveled when she meets the box `gt`A. 10 mB. Since there is no friction, the girl will not moveC. 16 mD. 4m
Lecithin is a (A) carbohydrate (B) phospholipid (C) nucleoside (D) protein

Let A and B be any two n × n matrices such that the following conditions hold : AB = BA and there exist positive integers k and l such that Ak = I (the identity matrix) and Bl = 0 (the zero matrix). Then- (A) A + B = I (B) det (AB) = 0 (C) det (A + B) ≠ 0 (D) (A + B)m = 0 for some integer m

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment