Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let A be a 2 × 2 matrix with non-zero entries and let A 2 = I , where I is 2 × 2 identity matrix.
Tr(a) = sum of diagonal elements of A and |A| = determinant of matrix A.
Statement -1 : Tr(a) = 0
Statement -2 : |A| = 1
Text Solution
Verified by ExpertsThe correct answer is:
B
Sol. Let A = 
; A 2 = 
= 
= 
⇒ a + d = 0 and a 2 + bc = 1
⇒ Tr(a) = 0
Statement-1 is true
Statement-2 |A| = ad – bc = – a 2 – bc = – 1
Statement-1 is true statement-2 is false.
Hence correct option is
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
Let A be a 2 × 2 matrix.
Statement-1 : adj(adj
Let a, b, c be such that b(a + c) ≠ 0. If + = 0. Then the value of 'n' is –
The number of 3 × 3 non-singular matrices, with four entries as 1 and all other entries as 0, is
Consider the system of linear equations :
x 1 + 2x 2 + x 3 = 3
2x 1 + 3x 2 + x 3 = 3
3x 1 + 5x 2 + …
Let A and B be two symmetric matrices of order 3.
Statement-1 : A(BA) and (AB)A are symmetric matri…
The number of values of k for which the linear equations
4x + ky + 2z = 0
kx + 4y + z = 0
2x + 2y +…