-1 2 and I is the unit matrix of order 2, than A² is equal to
A) 4A - 3I B) 3A+ 4I C) A- I D) A+ I
2) The multiplicative inverse of matrix 2 1
-7 4 is
A) 4 -1 B) 4 -1 C) 4 -7 D) -4 -1
-7 -2 -7 -2 7 2 7 -2
3) If A= 1 0 2 and Adj A= 5 a -2
-1 1 -2 1 q 0
0 2 1 -2 -2 b then the value of a and b are
A) a=-4, b= 1 B)a=-4, b= -1 C) a=4, b= 1 D) a=4, b= -1
4) If A= -1 0
0 2 then the value of A³ - A² is equal to
A) I B) A C) 2A D) 2I
5) If A= -x -y
z t , then transpose of adj A is
A) t z B) t y C) t -z D) none
-y -x. -z -x y -x
6) Assuming that the sums and products given below are defined, which of the following is not true for metrices?
A) AB= AC does not imply B= C B) A+ B= B+ A C) (AB)'= B' A' D) AB= O implies A= O or, B= O
7) If A= 3 5 & B= 1 17
2 0 0 -10 then |AB| is equal to
A) 80 B) 100 C) -110 D) 92
8) If A= 5 -2
3 1 find inverse of A is
A) -2/13 5/13 B) 1 2
1/13 3/13 -3 5
C) 1/11 2/11 1 3
-3/11 5/11 -2 5
9) If If A is a singular matrix of order n then A. (adj A) is equal to
A) a null matrix B) a row matrix C) a column matrix D) none
10) If A and B are two square metrices and A⁻¹ and B⁻¹ exist, then (AB) ⁻¹ is equal to
A)A⁻¹B⁻¹ B) AB⁻¹ C) A⁻¹B D) B⁻¹A⁻¹
11) If A= 5 6 -3
-4 3 2
-4 -7 2 then the co-factors of the elements of second row are
A) 3,3,11 B) 3,-3,11 C) -39,3,-11 D) 39,-3,11
12) If A= 1 2 & B= 1 2
2 3 2 1
3 4
Then,
A) both AB and BA exist B) neither AB nor BA exist C) AB exists but BA does not exist D) AB does not exist but BA exists
13) If A= 2 -1 & B= 1 0
0 1 -1 -1 then (A+ B)² is not equal to
A) A²+ AB+ BA+ B² B) A²+ AB+ BA+ B²I C) A²I + AB+ BA+ B² D) A²+ 2AB+ B²
14) If A be an n x n matrix and k any scalar, then det kA is equal to
A) k det A B) nᵏ det A C) kⁿdet A D) kn det A
15) If A= -1 2 & B= 5
2 -1 7 and AX= B, then X is equal to
A) 19 17 B)19/3 C) 19/3 17/3 D)19
17/3 17
16) If A is a square matrix of order 3x3 and k is a scalar, then adj(kA) is equal to which of the following?
A) k adjA B) k² adjA C) k³ adjA D) 2k adjA
17) If A= 0 1 2
1 2 3
3 1 1 and its inverse B=[b ᵢⱼ],then the element b₂₃ of matrix B is
A) -1 B) 1 C) -2 D) 2
18) If A= a b c & B= 1 2 3
d e f 2 3 4
g h i 3 4 5
D= -1 -2 & E= -4 -5 -6
-2 0 0 0 1
0 -4
And A= BCD then the value of e
A) 40 B) -40 C) -20 D) 20
19) If A= 1 2 & B= 3 8
3 4 7 2 and the relation 2X+ A= B, then the matrix X is
A) 2 6 B)1 -3 C) 1 3 D) 2 -6
4 -2 2 -1 2 -1 4 -2
20) If A= a 2
2 a and |A³|= 125, then the value of a is
A) ±2 B) ±3 C) ±5 D) 0
21) If A) 1 0 0
a 1 0
b c 1 find the Inverse of A
A)1 0 0 B)1 0 0 C) 1 -a ac- b D)1 0 0
-a 1 0 -a 1 0 0 1 -c -a 1 0 ac-b -c 1 -b -c 1 0 0 1 ac b 1
22) If A= 0 3 & B= 0 4a
4 5 3b 60 then the value of k, a and b are respectively
A) 12,9,16 B)9,12,16 C) 12,9,12 D) 16,12,9
23) If the matrix A satisfies the equation 1 3 x A = 1 1
0 1 0 -1 then which one of the following represents A?
A) 1 4 B) 1 4 C) 1 -4 D) 1 -2
-1 0 0 -1 1 0 0 -1
24) For any matrix A, if A⁻¹ exists then which of the following is not true?
A) (A⁻¹)⁻¹= A B) (A')⁻¹= (A⁻¹)' C) (A²)⁻¹ = (A⁻¹)² D) |A⁻¹|=|A|⁻¹
25) If A and B are two square metrices of the same order, than (A- B)² is equal to
A) A²- 2AB+ B² B) A²- AB - BA+ B² C) A²- 2BA+ B² D) A²+ 2AB+ B²
26) If A= -1 2 4 & B= -2 4 2
3 1 0 6 2 0
-2 4 2 -2 4 8 then which one of the following is correct?
A) B=-A B) B= 6A C) B= 4A D) B= -4A
27) For how many values of x in the closed interval [-4,-1], the matrix
3 -1+x 2
3 -1 x+2
x+3 -1 2 is singular?
A) 0 B) 1 C) 2 D) 3
28) If A= 7 1 2 & B= 3 C) 4
9 2 1 4 2
5 and the relation AB+ 2C is equal to
A) 43 B) 43 C) 45 D) 44
44 45 44 45
29) If A= 3 4
5 7 then the value of A(adjA) is equal to
A) I B) |A| C) |A|. I D) none
30) x+ y 2x+ z = 4 7
x- y 2z+ w 0 10 then the value of x,y,z and w are
A) 2,3,1,2 B) 2,2,3,4 C) 3,3,0,1 D) 2,2,4,3
31) The matrix 2 k -4
-1 3 4
1 -2 -3 is non singular if
A) k≠2 B) k≠3 C) k≠-3 D) k ≠ -2
32) If A= 3 2 & AC= 19 24
4 5 37 46 then the matrix is equal to
A) 3 4 B) 3 5 C) 5 4 D) 3 2
5 6 4 6 2 6 6 4
33) If A² - A + I= 0 then the inverse of matrix A is
A) A- I B) A+ I C) A D) I - A
34) Let A and B are two square metrices such that AB= A and BA = B. Then A² is
A) O B) I C) A D) B
35) if A= 4 2
-1 1 then the value of (A- 2I)(A - 3I) is
A) A B) I C) O D) 4I
36) if A= 1 -1 & B= a 1
2 -1 b -1 and A²+ B², then the value of a and b are
A) 4,1 B) 1,4 C) 0,4 D) 2,4
37) let A= a 0 & B= 1 0
1 1 5 1 if A²= B, then the value of a is
A)1 B) -1 C) 4 D) no real value of a
38) 0 7 4
-7 0 -5
-4 5 0 is
A) symmetric B) skew symmetric C) non singular D) orthogonal matrix
39) If A= 1 -1 1 & 10B= 4 2 2
2 1 -3 -5 0 b
1 1 1 1 -2 3 if B is the inverse of the matrix A, then the value of b is
A) 2 B) -1 C) -2 D) 5
40) If A= 0 0 -1
0 -1 0
-1 0 0 then the only correct statement about the matrix A is
A) A⁻¹ does not exist B) A= (-1) I C) A is a zero matrix D) A²= I
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