1) if A= 2 -1
-1 2 and I is the unit matrix of order 2, then 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) Assuming that the sums and products given below are defined, which of the following is not a true for matrices?
a) AB= AC doesn't imply B= C
b) A+ B = B+ A
c) (AB)'= B'A'
d) AB= 0 implies A= O or B= O
4) If A= 1 0 2 & Adj A= 5 a -2
-1 1 -2 1 1 0
0 2 1 -2 -2 b
Then the values of a and b are
a) -4,1 b) -4, -1 c) 4, 1 d) 4, -1
5) If A= -1 0
0 2 then the value of A³- A² is equal to
a) I b) A c) 2A d) 2I
6) If A= - x - y
z t then the transpose of adj A is
a) t z b) t y c) t -z d) none
-y - x -z -x y -x
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 the inverse of A
9) If A is 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= 3 -5
-4 2 then find the value of A²- 5A is equal to
a) I b) 14I c) O d) none
11) 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 exist
12) 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
13) If A be an n × n matrix and k any scalar then det. kA is equal to
a) k detA b) nᵏdetA c) kⁿ detA d) kn detA
14) If A= 1 2
3 -5 find inverse of 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≠ O and B≠ O are two 2 x 2 matrices such that AB= O, then which of the following is correct?
a) detA= 0 or detB= 0
b) detA= 0 and detB= 0
c) detA= 0 = detB≠ 0 d) none
17)
1a 2b 3d 4c 5c 6c 7d 9a 10b 11c 12d 13c 15b 16b
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