Transpose of a Matrix

Q. If A', B' are transpose matrices of the square matrices A, B respectively , then (AB)' is equal to

1. A'B'
2. B'A'
3. AB'
4. BA'

Q. The total number of $3\times 3$ matrices $A$ having entries from the set $\{0,1,2,3\}$ such that the sum of all the diagonal entries of $A{A}^T$ is $9$, is equal to

Q. $A=[a_{ij}{]}_{n\times n}$ and $a_{ij}=i^2-j^2$ then A is necessarily

1. symmetric matrix
2. skew symmetric matrix
3. zero matrix
4. a unit matrix

Q. Which among the following would be obtained on simplifying the expression $(A^{T}BA{)}^T$.

1. $A^T{B}^T{A}^T$
2. $A^T{B}^{T}A$
3. $A{A}^T{B}^T$
4. $B^T{A}^{T}A$

Q. If $A=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$ then AA' =

1. $Noneofthese$
2. $\left[\begin{array}{c}1\\ 3\\ 3\end{array}\right]$
3. $14$
4. $\left[\begin{array}{ccc}1& 2& 3\\ 2& 4& 6\\ 3& 6& 9\end{array}\right]$

Q.

If A and B are two square matrices which are skew symmetric then$(AB{)}^T$ equals to

1. AB
2. BA
3. -AB
4. -BA

Q.

If A and B are two square matrices which are skew symmetric then $(AB{)}^T$ equals to

1. AB
2. BA
3. -AB
4. -BA

Q. If A is a $3\times 3$ non-singular matrix such that $A{A}^T=A^{T}AandB=A^{-1}{A}^T,thenB{B}^T$ is equal to

1. I
2. $B^{-1}$
3. I + B
4. ${\left(B^{-1}\right)}^T$

Q.

$(AB{)}^T=A^T{B}^T$. The statement is

1. True

2. False

Q.

If $A=\left[\begin{array}{cccc}1& 0& 2& 3\\ 4& 2& 6& 4\end{array}\right]$ then fourth element of second column of $A^T$ =

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