Multiple Choice QuestionsLet A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A2= I.
Statement −1: If A ≠ I and A ≠ − I, then det A = − 1.
Statement −2: If A ≠ I and A ≠ − I, then tr (A) ≠ 0.
Statement −1 is false, Statement −2 is true
Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.
Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.
Let A be a square matrix all of whose entries are integers. Then which one of the following is true?
If det A = ± 1, then A–1 exists but all its entries are not necessarily integers
If detA ≠ ± 1, then A–1 exists and all its entries are non-integers
If detA = ± 1, then A–1 exists and all its entries are integers
If detA = ± 1, then A–1 exists and all its entries are integers
Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx and z = bx + ay. Then a2 + b2 + c2 + 2abc is equal to
2
-1
0
0
If D = 
for x ≠ 0, y ≠ 0 then D is
divisible by neither x nor y
divisible by both x and y
divisible by x but not y
divisible by x but not y
Let 
a , b ∈ N. Then
there cannot exist any B such that AB = BA
there exist more than one but finite number of B’s such that AB = BA
there exists exactly one B such that AB = BA
there exists exactly one B such that AB = BA
If the system of linear equations
x + ky + 3z = 0
3x + ky – 2z = 0
2x + 4y – 3z = 0
has a non-zero solution (x,y,z), then xz/y2 is equal to
30
-10
10
-30
then adj (3A2 + 12A) is equal to
If |A2| = 25, then |α| equals
