Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Determinants · Assertion Reason1 Marksassertion_reason

Class 12 Maths · Determinants · Assertion Reason #23

Assertion: If A is 3×3, det(A)≠0 and det(5A)=Kdet(A), then K=125. Reason: For any n×n matrix A and scalar k, det(kA)=kⁿdet(A).

✅ Step-by-Step Solution

Final Answer: Option (A): Both A and R are true, and R correctly explains A.
  1. The scaling law with n=3,k=5 gives det(5A)=125det(A). Since det(A)≠0, K=125.

Master Chapter 4: Determinants

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Determinants.
📘 Chapter Notes & All Exercises 🚀 Open in Interactive Workspace →
← Previous Question
Assertion: For A=\(\begin{bmatrix}5−x & x+1\\2 & 4\end{bmatrix}\), A…
Next Question →
Assertion: If \(\begin{vmatrix}x & 2\\18 &…

More Practice Questions in Determinants

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

Related Questions in Determinants

Class 12 Determinants · Mcq Single Correct
If \(\begin{vmatrix}2 & 4\\5 & 1\end{vmatrix}\)=\(\begin{vmatrix}2x & 4\\6 &…
Class 12 Determinants · Mcq Single Correct
The area of the triangle with vertices (−3,0),(3,0),(0,k) is 9 square units. Find k.
Class 12 Determinants · Mcq Single Correct
Let f(x)=\(\begin{vmatrix}0 & x−a & x−b\\x+a & 0 & x−c\\x+b & x+c & 0\end{vmatrix}\). Which…
Class 12 Determinants · Mcq Single Correct
If \(\begin{vmatrix}2 & 3 & 2\\x & x & x\\4 & 9 & 1\end{vmatrix}\)+3=0, find x.
Class 12 Determinants · Mcq Single Correct
If x=−4 is a root of \(\begin{vmatrix}x & 2 & 3\\1 & x & 1\\3 & 2 & x\end{vmatrix}\)=0, find…
Class 12 Determinants · Mcq Single Correct
For a 3×3 real matrix A, det(Aᵀ)=−3. Find det(AAᵀ).