Matrices and determinants

MATRICES AND DETERMINANTS-MATHS PRACTICE QUIZ


1.If A is an invertible matrix of order 2 and then det(inverse of A) is
equal to
Answer: 1/det(A)

2.If for the non-singular matrix A,A^2=I and then find the inverse of A
Answer: A

3.What type of matrix has only one element?
Answer: Scalar

4.Rank of a matrix is denoted by the symbol of
Answer:

5.A system of linear equations having at least one solutions is said to
be
Answer: Consistent

6.If A is a square matrix of order 4 and |A|=4 then |2A| will be
Answer:64

7.If for some alpha and beta in R, the intersection of the following
three planes x+4y-2z=0,x+7y-5z=0,x+5y+z=0 is a line R3,then is equal to
Answer: -3

8. Let A and B be two 3*3 real matrices such that (A^2-B^2) is invertible
matrix. If A^5=B^5 and A^3 B^2=A^2 B^3, then the value of the determinant
of matrix A^3+B^3 is equal to
Answer:0

9.If A is a 3 * 3 matrix and |A|=2,then|3adj(|3A|A^2)|is equal to
Answer:3^11 6^10

10.Let A be a 3*3 matrix such that A^2 =5A-6I.If |A|=30, then Tr(7A)
equals
Answer:70

11.Let A be a 2*2 real matrix and I be the identify matrix of order 2. If
the roots of the equation |A-XI|=0 be -1 and 3, then the sum of the
diagonal elements of the matrix A^2 is
Answer:10

12.Number of skew symmetric matrices of order 3*3 with each entry 1 or 2
is
Answer:8

13.How many 3*3 matrices M with entries from {0,1,2} are there for which
the sum of the diagonal entries of M^T*M is 5?
Answer:198

14.Let A and B be n*n matrices such that BA + B^2 = I-BA^2,where I is n*n
identify matrix