1. For a non-singular matrix A, $(A^{-1})^{-1}=$______
2. If A is a non-singular matrix, then $((A)^t)^t=$________
3. The Rank of the matrix $\begin{bmatrix} 1 & 0 & 3 \end{bmatrix}$ is
4. If $A=\begin{bmatrix} 2 & 1 \\ 6 & 3 \end{bmatrix}$ then cofactor of 6 is:
5. For non-homogeneous system of equations; the system is inconsistent if;
6. $A=\begin{bmatrix} 1 & -2 & 3 \\ 0 & 0 & 1 \\ 4 & 5 & 2 \end{bmatrix}$ then $M_{13}=?$
7. A square matrix $A=[a_{ij}]$ is upper-triangular matrix if ________
$a_{ij}\,\neq\,0, \forall \, i
$a_{ij}=0, \forall \, i=j$
$a_{ij}\,\neq\,0, \forall \, i>j$
$a_{ij}=0, \forall \, i>j$
None
8. A matrix of order $\mathbf{1} \times \mathbf{n}$ is called
9. If $AX=B$ represents the system of non-homogeneous linear equation then $X=$________
10. Let $A=\begin{bmatrix} 1 & 2 & 3x \\ 2 & 3 & 6x \\ 3 & 5 & 9x \end{bmatrix}$ then $|A|$ is equal to_____
11. Rank of the matrix $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{bmatrix}$ is
12. Rank of matrix $\begin{bmatrix} 1 \\ 1 \\ 1 \\ 0 \end{bmatrix}$ is
13. For an element $A_{ij}$ of a square matrix A;
14. If the matrix $\begin{bmatrix} \lambda & 4 \\ 1 & 2 \end{bmatrix}$ is singular then $\lambda=?$
15. If $A$ is any matrix then $A$ and $A^t$ are always comfortable for;
16. If the matrix $\begin{bmatrix} x+1 & 8 \\ 1 & x-1 \end{bmatrix}$ is singular then $x=?$
17. For a skew-symmetric matrix the diagonal elements must be:
18. If matrix $A=\begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 1 & -1 & 1 \end{bmatrix}$ then the cofactor $A_{32}=?$
19. A is a square matrix then skew matrix is
20. Transpose of a diagonal Matrix is:
21. If $\begin{vmatrix} k & 4 \\ 4 & k \end{vmatrix}=0$ then $k=?$
22. If order of $A$ is $\mathbf{m} \times \mathbf{n}$ and order of $B$ is $\mathbf{n} \times \mathbf{p}$ then order of $(AB)^{t}$ is:
23. If A and B are non-singular matrices, then $(AB)^{-1}$ is equal to:
24. For non-homogeneous system of linear equations, system $AX=B$, solution is possible if _________
25. If A is square matrix of order $\mathbf{4} \times \mathbf{3}$ then number of elements in each column of $A$ is
26. If $A=\begin{bmatrix} d & b \\ -c & a \end{bmatrix}$ then $adj(A) =?$
27. If order of $A$ is $\mathbf{m} \times \mathbf{n}$ and order of $B$ is $\mathbf{n} \times \mathbf{p}$ then order of $AB$ is:
28. $\begin{vmatrix} 2 & 3 & 0 \\ 3 & 9 & 6 \\ 2 & 15 & 1 \end{vmatrix}=a\begin{vmatrix} 2 & 1 & 0 \\ 1 & 1 & 2 \\ 2 & 5 & 1 \end{vmatrix}$ then $a=$
29. A system of non-homogeneous equation having infinite many solutions can be solving by using:
30. The inverse of a square matrix exists if $A$ is:
31. System of homogeneous linear equations has non-trivial solution if:
32. A square matrix $A=[a_{ij}]$ is lower-triangular matrix if ________
$a_{ij}=0, \forall \, i>j$
$a_{ij}\,\neq\,0, \forall \, i
$a_{ij}=0, \forall \, i
$a_{ij}\,\neq\,0, \forall \, i>j$
None
33. If A is square matrix then which is true.
34. For the square matrix $A$ of order $\mathbf{3} \times \mathbf{3}$ and $|A|=9$; $A_{21}=2$; $A_{22}=3$; $A_{23}=-1$; $a_{21}=1$; $a_{23}=2$, the value of $a_{22}$ is;
35. The matrix $\begin{bmatrix} 1 & 2 & 0 \\ 0 & 1 & 4 \\ 0 & 0 & 6 \end{bmatrix}$
36. If A is non-singular square matrix, then $AA^{-1}$ equals ______
37. If $A$ is a square matrix of order $\mathbf{3} \times \mathbf{3}$ and $|A|=3$ then value of $|adjA|$ is;
38. If two rows of any square matrix are identical, then the value of determinant is ________
39. If two rows of a square matrix A are interchanged then determinant of resulting matrix is
40. The trivial solution of homogeneous linear equations is;
41. If a system has a unique solution or infinitely many solutions then the system is called_______
42. For any non-singular matrix A, $A^{-1}$ is:
43. For homogeneous linear equations, system $AX=O$ non-trivial solution is possible if $|A|=$ _______
44. If A is a skew symmetric then $A^2$ will be
45. If A is skew symmetric then $A^2$ will be
47. If $A=\begin{bmatrix} 1 & -2 & 3 \\ 0 & 0 & 1 \\ 4 & 5 & 2 \end{bmatrix}$ then $M_{13}=$
48. If $A$ is a row matrix of order $\mathbf{1} \times \mathbf{n}$ then order of $A^t A$ is:
49. If A is a matrix of order $\mathbf{3} \times \mathbf{2}$ then order of $A^{t}A$ is _________
50. If all entries of a row (column) of a square matrix A are zero, then |A| equals ________
51. For a system of non-homogeneous equations with three variables system will have unique solution if;
52. If $\begin{vmatrix} a & b \\ c & d \end{vmatrix}$ then $\begin{vmatrix} c & d \\ a & b \end{vmatrix}=?$
53. If $A$ is a square matrix of order $3 \times 3$ then $|KA|=?$
54. if $|A|=5$ then $|A^t|=$?
55. The inverse of a unit matrix is ___________
56. The value $A=\begin{vmatrix} 1 & 12 & 25 \\ 0 & 3 & 15 \\ 0 & 0 & 8 \end{vmatrix}=?$
57. The cofactor of an element $a_{ij}$ denoted by $A_{ij}=$______.
58. The solution of the system $a_{1}+b_{1}y=0$ and $a_{2}+b_{2}y=0$ is called _________
59. If A is non-singular matrix, $(A^t)^t=$______.
60. Rank of the matrix $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ is __________
