CBSE Class 12 Mathematics 2026 Main Paper 65/3/3 · Q91 Marksidempotent_matrices
CBSE Class 12 Mathematics 2026 Main Paper 65/3/3 · Question 9 (Matrices)
For a nonzero square matrix A, suppose A²=A and (I−A)³=xA+I. Find x.
✅ Step-by-Step Solution
Final Answer: −1
- Since A²=A, (I−A)²=I−A and (I−A)³=I−A. Thus xA=−A and x=−1 for A≠0.
Master Chapter 3: Matrices
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Matrices.
← Previous Question
If [2 1]X=[3 4 5], find the order of X.
Next Question →If A adj(A)=3I₃, find det(2A).
All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/3/3
Related Questions in Matrices
Class 12 Matrices · Mcq Single Correct
Let A be a 2×2 matrix with aᵢⱼ=1 for i≠j and 0 for i=j. Find A².
Class 12 Matrices · Mcq Single Correct
Let A=\(\begin{bmatrix}\cos\alpha & -\sin\alpha\\\sin\alpha & \cos\alpha\end{bmatrix}\)…
Class 12 Matrices · Mcq Single Correct
If \(\begin{bmatrix}2a+b & a−2b\\5c−d & 4c+3d\end{bmatrix}\)=\(\begin{bmatrix}4 & -3\\11 &…
Class 12 Matrices · Mcq Single Correct
How many 3×3 matrices have every entry either 2 or 0?
Class 12 Matrices · Mcq Single Correct
Find x+y for constants x,y such that the identity A⁻¹=xA+yI holds for every real square…
Class 12 Matrices · Mcq Single Correct
If \(\begin{bmatrix}2 & 0\\5 & 4\end{bmatrix}\)=P+Q, where P is symmetric and Q…