Question
Let A= [ array ccc 0 & 2 & -3 \\ -2 & 0 & 1 \\ 3 & -1 & 0 array ] and B be a matrix such that B(I-A)=I+A. Then the sum of the diagonal elements of B ^ T B is equal to \_\_\_\_.
JEE Main
Mathematics
Matrices
2026
JEE Main 2026 (23 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
A is skew-symmetric (A^T = -A). From B(I-A) = I+A: B = (I+A)(I-A)^ -1 . B^T = ((I-A)^T)^ -1 (I+A)^T = (I+A)^ -1 (I-A). Since A is skew-symmetric, (I-A) and (I+A) commute: (I-A)(I+A) = I - A^2 = (I+A)(I-A). B^TB = (I+A)^ -1 (I-A)(I+A)(I-A)^ -1 = (I+A)^ -1 (I+A)(I-A)(I-A)^ -1 = I. Trace of B^TB = tr (I) = 3.
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