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Do you want to solve the problem if Last Digit of (detA)²⁰²⁵ = 1, Find k!, the JEE Advanced & Olympiad Number Theory Trick, you are at the right place.

"Given the matrix A with rows (5,2,7), (7,k,5), (–4,–2,–6), find the rational value of k such that the last digit of (detA)²⁰²⁵ is 1."

Struggling with last digit problems involving matrices and huge exponents? You're not alone! In this video, IITina breaks down a rare but powerful JEE Advanced & Maths Olympiad-level problem:

"Given the matrix A with rows (5,2,7), (7,k,5), (–4,–2,–6), find the rational value of k such that the last digit of (detA)²⁰²⁵ is 1."

Answer is -5/2 - 5m.

Learn a number theory trick for JEE Advanced with modular arithmetic and linear algebra to find the last digit of (detA)^2025. Let's solve for k together!

We’ll solve it step by step using:
✅ Determinant properties of 3×3 matrices
✅ The identity (det A)ⁿ
✅ Modular arithmetic (mod 10) and units digit cycles
✅ Number theory insights for odd exponents like 2025
✅ Why k must be rational (not integer!) — and how to find it

This problem blends linear algebra and number theory — exactly the kind of interdisciplinary thinking tested in JEE Advanced, INMO, RMO, and CSIR NET Mathematical Sciences.

Whether you're preparing for:

JEE Main / JEE Advanced 2025
Maths Olympiads (RMO, INMO, IMO)
CSIR NET / GATE Mathematics
Or just love elegant math puzzles…
…this video will sharpen your problem-solving intuition and teach you a repeatable framework for tackling "last digit of large powers" questions.

The playlists and links for all videos are given as below :

MATHEMATICS BY IITIAN

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Channel Name : MATHS&SCIENCE BY IITIAN
Handle : @mathsciencebyiitian
Email : [email protected]

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