Sarthaks Test
0 votes
11 views
in Determinants by (15.2k points)
closed by

If A and B are square matrices or order 2, then det (A + B) = 0 is possible only when 

A. det (A) = 0 or det (B) = 0 

B. det (A) + det (B) = 0 

C. det (A) = 0 and det (B) = 0 

D. A + B = 0

1 Answer

+1 vote
by (14.5k points)
selected by
 
Best answer

D. A + B = 0

We are given that, 

Matrices A and B are square matrices. 

Order of matrix A = 2 

Order of matrix B = 2 

Det (A + B) = 0 

We need to find the condition at which det (A + B) = 0. 

Let, 

Matrix A = [aij] Matrix B = [bij

Since their orders are same, 

We can express matrices A and B as,

A + B = [aij + bij

⇒ |A + B| = |aij + bij| …(i) 

Also, 

We know that,

Det (A + B) = 0 

That is, 

|A + B| = 0 

From (i), 

|aij + bij| = 0 

If 

⇒ [aij + bij] = 0 

Each corresponding element is 0. 

⇒ A + B = 0

Thus, 

det (A + B) = 0 is possible when A + B = 0.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...