Matrices & Determinants · JEE Main previous year questions

2010 2 questions

1. Q122010 · 25 Apr 2010 · Shift 1

   Let $A$ be a $2\times 2$ matrix with non-zero entries and let $A^2=I$, where $I$ is $2\times 2$ identity matrix. Define $\mathrm{Tr}(A)=$ sum of diagonal elements of $A$ and $|A|=$ determinant of matrix $A$. Statement- 1: $\mathrm{Tr}(A)=0$. Statement- 2: $|A|=1$ .

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

   Answer: B

2. Q142010 · 25 Apr 2010 · Shift 1

   The number of $3\times 3$ non-singular matrices, with four entries as 1 and all other entries as 0, is :

   1. A.$5$
   2. B.$6$
   3. C.at least 7
   4. D.less than 4
   Show answer

   Answer: C