InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
For a matrix `M=[(3/5, 4/5),(x,3/5)]`, If `M^-1=M^T` then `x=`A. `-3/5`B. `-4/5`C. `4/5`D. `3/5` |
| Answer» Correct Answer - B | |
| 2. |
A square matrix A is used to be an idempotent matrix if `A^(2) = A`. If A is an idempotent matrix and B = I -A, then-A. AB = 0B. BA`ne`0C. `B^(2)` = ID. `AB = I_(n)` |
| Answer» Correct Answer - A | |
| 3. |
If `A` and `B` are two matrices such that `AB=B` and `BA=A`, then `A^2+B^2=`A. |A| = |B|B. |A| = -|B|C. |A| = 2|B|D. A is invertible if and only if B is invertible |
| Answer» Correct Answer - B::D | |
| 4. |
If A is a matrix of size `nxxn` such that `A^(2) + A + 2I` = O thenA. A is non-singularB. `A ne O`C. |A| = OD. `A^(-1) = (-1)/(2)(A + I)` |
| Answer» Correct Answer - A::B::C::D | |
| 5. |
If A be a proper orthogonal matrix, then-A. |A| = 0B. |A|=1C. |A|=2D. |A|=3 |
| Answer» Correct Answer - B | |
| 6. |
If A be an orthogonal matrix, then the value of `A^(-1)` will be -A. AB. `A^(T)`C. `A^(2)`D. `A^(3)` |
| Answer» Correct Answer - B | |
| 7. |
If a,b,c, are non-zero real numbers, then the inverse of matrix A = `[(a,0,0),(0,b,0),(0,0,c)]` is -A. `[(a^(-1),0,0),(0,b^(-1),0),(0,0,c^(-1))]`B. abc`[(a^(-1),0,0),(0,b^(-1),0),(0,0,c^(-1))]`C. `[(a,0,0),(0,b,0),(0,0,c)]`D. `(1)/(abc)[(1,0,0),(0,1,0),(0,0,1)]` |
| Answer» Correct Answer - A | |
| 8. |
If `A` is a `2×2` square matrix with `|A|=3` then find `|3A|`A. a = -2B. a = 2, b = 1C. b = -1D. b = 1 |
| Answer» Correct Answer - A::C | |
| 9. |
If `[(x+y,2x+z),(x-y,2z+w)]=[(4,7),(0,10)]` then the values of x, y, z and w are -A. singularB. non-singularC. skey-symmetricD. a square matrix |
| Answer» Correct Answer - B::C::D | |
| 10. |
If A and B are two invertible matrices of the same order, then adj (AB) is equal to -A. adj (A) adj (B)B. |B||A|`B^(-1)A^(-1)`C. |B||A|`A^(-1)B^(-1)`D. |A||B|`(AB)^(-1)` |
| Answer» Correct Answer - A::B::D | |
| 11. |
If `A` is a `3×3` square matrix with `|A|=5` if `B=4A^2`then find `|B|`A. Statement-I is True, Statement-II is True: Statement-II is a correct expianation for Statement-I.B. Statement-I is True,Statement-II is True: Statement-II is not a correct explanation for Statement-I.C. Statement-I is True, Statement-II is False.D. Statement-I is False, Statement-II is True. |
| Answer» Correct Answer - D | |
| 12. |
If A = `[(3+2i, i),(-i,3-2i)]` then find `A^-1`A. Statement-I is True, Statement-II is True: Statement-II is a correct expianation for Statement-I.B. Statement-I is True,Statement-II is True: Statement-II is not a correct explanation for Statement-I.C. Statement-I is True, Statement-II is False.D. Statement-I is False, Statement-II is True. |
| Answer» Correct Answer - C | |
| 13. |
A square matrix A is used to be an idempotent matrix if `A^(2) = A`. If A, B and A + B are idempotent matrices, then-A. AB = BA = 0B. AB = BA = `I_(n)`C. AB = BA`ne`0D. AB = BA`neI_(n)` |
| Answer» Correct Answer - A | |
| 14. |
Two `nxxn` square matrices A and B are said to be similar if there exists a non - singular matrix C such that `C^(-1)` AC = B .If A and B are similar matrices such that det(A) = 1, then -A. de(B) = 1B. det(A) + det(B) = 0C. det(B) = -1D. none of these |
| Answer» Correct Answer - A | |
| 15. |
Two `nxxn` square matrices A and B are said to be similar if there exists a non - singular matrix C such that `C^(-1)` AC = B . If A and B are two singular matrices, then-A. det(A) = det(B)B. det(A) + det(B) = 0C. det(AB) = 0D. none of these |
| Answer» Correct Answer - A | |
| 16. |
A square matrix A is called singular if -A. |A|`gt` 0B. |A|`lt`C. |A| = 0D. |A| = a complex number |
| Answer» Correct Answer - C | |
| 17. |
`(Adj.A)/(|A|)`=A. `A^(T)`B. `A^(-1)`C. `(A^(-1))^(T)`D. `(A^(T))^(-1)` |
| Answer» Correct Answer - B | |
| 18. |
`(AB)^(-1)` =A. `A^(-1) B^(-1)`B. `A^(-1)`BC. `B^(-1)A^(-1)`D. A`B^(-1)` |
| Answer» Correct Answer - C | |
| 19. |
Matrices A and B will be inverse of each other only if-A. AB = BA`ne` IB. AB = BA = OC. AB = o , BA = ID. AB = BA = I |
| Answer» Correct Answer - D | |
| 20. |
If A is an invertible matrix of order 3 and |A| = 5, then the value of |adjA| is equal to-A. 20B. 21C. 24D. 25 |
| Answer» Correct Answer - D | |