The rank of the matrix `[[r,a,b,0],[0,c,d,1],[1,a,b,0],[0,c,d,1]]`
is: (A) `1` (B) `2` (C) `3` (D) `4`

If the rank of the matrix A= [(1,2,3,0),(2,4,3,2),(3,2,1,3),(6,8,7,alpha)] is 3 then a= (A) -5 (B) 5 (C) 4 (D) 4

If [[x,1]][[1,0],[2,0]]=0 ,then x equals (A) 0 (B) -2 (C) -1 (D) 2

a^0 is equal to.... (A) 0 (B) 1 (C) -1 (D) a

If the matrix A=[[1,2,3,0],[2,4,3,2],[3,2,1,3],[6,8,7,alpha]] is of rank 3 then alpha= (A) -5 (B) 5 (C) 4 (D) -4

If A= [[a,b],[c,d]] and I= [[1,0],[0,1]] then A^(2)-(a+d)A=

The inverse of the matrix [(1,0,0),(a,1,0),(b,c,1)] is (A) [(1,0,0),(-a,1,0),(b,c,1)] (B) [(1,0,0),(-a,1,0),(ac,b,1)] (C) [(1,-a,ac-b),(-0,1,-c),(0,0,1)] (D) [(1,0,0),(-a,1,0),(ac-b,-c,1)]

If for a matrix A,A^2+I=0, where I is an identity matrix then A equals (A) [(1,0),(0,1)] (B) [(-1,0),(0,-1)] (C) [(1,2),(-1,1)] (D) [(-i,0),(0,-i)]

If agt0, bgt0, cgt0 and the minimum value of a^2(b+c)+b^2(c+a)+c^2(a+b) is kabc, then k is (A) 1 (B) 3 (C) 6 (D) 4

If A=[(1,0,0),(0,1,0),(a,b,-1)] then A^2 is equal to (A) null matrix (B) unit matrix (C) -A (D) A

The matrix A=[(-5,-8,0),(3,5,0),(1,2,-1)] is (A) idempotent matrix (B) involutory matrix (C) nilpotent matrix (D) none of these