Question 1 :
A= $$\begin{bmatrix} 1&2&3\\4&5&6\\7&8&9\end{bmatrix}$$.B is matrix obtained by subtracting $$4\ times 1^{st}\ row from \ 2^{nd} \ row$$ of A.C is matrix obtained by subtracting $$7 \ times \ 1^{st}\ row\ from\ 3^{rd} row$$, then $$C$$ is 
Question 2 :
If $$A=\begin{bmatrix} 0 & a+1 & b-2 \\ 2a-1 & 0 & c-2 \\ 2b+1 & 2+c & 0 \end{bmatrix}$$ is skew symmetric then $$a+b+c$$=
Question 3 :
The system $$\begin{pmatrix} 1 & -1 & 2 \\ 3 & 5 & -3 \\ 2 & 6 & a \end{pmatrix}\begin{pmatrix} x \\ y \\ z \end{pmatrix}=\begin{pmatrix} 3 \\ b \\ 2 \end{pmatrix}$$ has no solution, if
Question 4 :
If $$A$$ and $$B$$ are symmetric matrices of order $$\displaystyle n,\left( A\neq B \right) $$, then<br/>
Question 5 :
$$A=\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta\end{bmatrix}$$ and $$AB=BA=I$$, then B is equal to
Question 6 :
If $$A=\begin{bmatrix} 2 & x-3 & x-2 \\ 3 & -2 & -1 \\ 4 & -1 & -5 \end{bmatrix}$$ is a symmetric matrices then $$x=$$
Question 7 :
If $$A=\begin{bmatrix} 3 & x \\ y & 0 \end{bmatrix}$$ and $$A={A}^{T}$$ then
Question 8 :
If $$A$$ and $$B$$ are two matrices such that $$A+B$$ and $$AB$$ are both defined, then
Question 9 :
If $$A = \begin{bmatrix}\cos \theta & -\sin \theta\\ \sin \theta & \cos \theta \end{bmatrix}$$, then the matrix $$A^{-50}$$ when $$\theta = \dfrac {\pi}{12}$$, is equal to<br>
Question 11 :
If the matrix $$AB$$ is a zero matrix, then which one of the following is correct?
Question 12 :
If A is any square matrix, then $$(A\, +\, A^T)$$ is a ............ matrix
Question 13 :
If $$A=([1\ \  2\ \  3\ \  4]$$ and $$AB = [3 \ \ 4\ \  -1$$] then the order of<br/>matrix B is 
Question 15 :
If <i>A </i>is an invertible matrix, then det $$\displaystyle \:\left ( A^{-1} \right )$$ is equal to
Question 16 :
If $$A=\displaystyle \left[ \begin{matrix} 1 & -6 & 2 \\ 0 & -1 & 5 \end{matrix} \right] $$ and $$\displaystyle B=\left[ \begin{matrix} 2 \\ 1 \end{matrix} \right] $$, then $$AB$$ equals
Question 17 :
$$\begin{bmatrix} 1&2&3\\4&5&6\\7&8&9\end{bmatrix}$$The new matrix obtained after  adding $$2^{nd} \  row \ to\  3\ times\  3^{rd} \ row $$ is
Question 20 :
If $$\displaystyle [A]\neq 0 $$ then which of the following is not true?<br>
Question 21 :
Assertion: Determinant of a skew-symmetric matrix of order of $$3$$ zero.
Reason: For any matrix $$A$$, $$det(A^{T})=det(A)$$ and $$det(-A)=-det(A)$$
Question 22 :
If $$A$$ is a $$3\times 3$$ skew symmetric matrix, then trace of $$A$$ is equal to
Question 23 :
$$A=\begin{bmatrix} 2&2&1\\0&1&4\\0&2&6\end{bmatrix}$$, $$B=\begin{bmatrix} 2&2&1\\0&1&4\\0&0&1\end{bmatrix}$$To obtain B from the matrix A, order of operations would be   
Question 24 :
Let a matrix $$A$$ is both symmetric and skew-symmetric then the matrix $$A$$ is
Question 25 :
If $$\begin{bmatrix} x & y \\ u & v \end{bmatrix}$$ is symmetric matrix, then
Question 26 :
If a $$3\times 3$$ matrix $$A$$ has its inverse equal to $$A$$, then $${A}^{2}$$ is equal to
Question 27 :
If $$P=\begin{bmatrix} 0 & 4 & -2 \\ x & 0 & -y \\ 2 & -8 & 0 \end{bmatrix}$$ is a skew-symmetric matrix, then x-y =<br/>
Question 28 :
A= $$\begin{bmatrix} 1&2&3\\4&5&6\\7&8&9\end{bmatrix}$$. B is matrix obtained by subtracting $$4 \ times \ 1^{st}\ row\ from \ 2^{nd} \ row$$ of A. Find matrix B
Question 29 :
If $$A$$ is any matrix, then the product $$AA$$ is defined only when A is a matrix of order $$m \times n$$ where : <br/>
Question 31 :
The inverse of $$\begin{bmatrix} 1 & a & b \\ 0 & x & 0 \\ 0 & 0 & 1 \end{bmatrix}$$ is $$\begin{bmatrix} 1 & -a & -b \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$$ then $$x=$$
Question 32 :
If $$A$$ is a matrix of order $$3\times 4$$, then both $${AB}^{T}$$ and $${B}^{T}A$$ are defined if order of $$B$$ is
Question 33 :
If $$A=\begin{bmatrix} a & b & c \\ x & y & z \\ l & m & n \end{bmatrix}$$ is a skew-symmetric matrix, then which of the following is equal to x+y+z ?<br/>
Question 34 :
If $$5A=\begin{bmatrix} 3 & -4\\ 4 & x\end{bmatrix}$$ and $$AA^T=A^TA=I$$ then $$x=?$$
Question 35 :
If $$A$$ is a skew symmetric matrix then $$ \displaystyle A^{T} $$ 
Question 36 :
If $$\mathrm{A}$$ is skew-symmetric matrix and $$\mathrm{n}$$ is even positive integer, then $$\mathrm{A}^{\mathrm{n}}$$ is<br/>
Question 38 :
If $$A =\begin{bmatrix}-i & 0\\0& i\end{bmatrix}$$, then $$A' \:A$$ is equal to<br><br>
Question 39 :
If $$A$$ is skew-symmetric matrix and $$n$$ is odd positive integer, then $$A^n$$ is<br>
Question 40 :
If $$A=\begin{bmatrix} 3 & 4 \\ 5 & 6 \\ 7 & 8 \end{bmatrix}$$ and $$B=\begin{bmatrix} 3 & 5 & 7 \\ 4 & 6 & 8 \end{bmatrix}$$, then which one of the following is correct?
Question 42 :
Consider the following statements in respect of the matrix $$A = \begin{bmatrix} 0 & 1 & 2\\ -1 & 0  & -3 \\ -2 & 3 & 0 \end{bmatrix}$$ :<br/>1. The matrix A is skew-symmetric. <br/>2. The matrix A is symmetric. <br/>3. The matrix A is invertible.<br/>Which of the above statements is/are correct ? <br/>
Question 43 :
If $$A$$ and $$B$$ are skew symmetric matrices of order n then $$A+B$$ is<br>
Question 45 :
If A is a square matrix of order 5 and $$9A^{-1}=4A^T$$ then |adj (adj (adj A))I (where $$A^{-T}$$ and adj(A) denotes the inverse, transpose and adjoint of matrix A respectively) contains: $$(log 3 =0.477,log 2 = 0.303)$$
Question 46 :
$$A=\begin{bmatrix} a & b \\ 0 & c \end{bmatrix}$$ then $${A}^{-1}+(A-aI)(A-cI)=$$
Question 47 :
If $$A$$ is square matrix such that $${A^2} = 1$$ then $${A^{ - 1}} = ?$$
Question 49 :
If $$A$$ and $$B$$ are two matrices such that $$AB = B$$ and $$BA = A$$, then $$A^2+B^2$$ equals
Question 50 :
If $$A=\begin{bmatrix} \cos { \theta } & -\sin { \theta } \\ \sin { \theta } & \cos { \theta } \end{bmatrix}$$, then $$A{A}^{T}$$ equals
