Question
Let A= [ array ll 3 & -4 \\ 1 & -1 array ] and B be two matrices such that A^ 100 =100 B+I. Then the sum of all the elements of B ^ 100 is \_\_\_\_
JEE Main
Mathematics
Matrices
2026
JEE Main 2026 (28 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 = I + bmatrix 2 & -4 \\ 1 & -2 bmatrix , let M = bmatrix 2 & -4 \\ 1 & -2 bmatrix M^2 = bmatrix 0 & 0 \\ 0 & 0 bmatrix = M^3 = M^4 = = M^ 100 A^ 100 = (I + M)^ 100 = _ r=0 ^ 100 100 r M^r I A^ 100 = I + 100M = I + 100B M = B M^ 100 = B^ 100 = bmatrix 0 & 0 \\ 0 & 0 bmatrix
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