matrix Multiplication

Q. If A = $\left[\begin{array}{cc}1& 5\\ 6& 2\end{array}\right]$ and B = $\left[\begin{array}{cc}3& 7\\ 8& 4\end{array}\right]$, then $A{B}^T$ is equal to

1. $$\left[\begin{array}{cc}38& 28\\ 32& 56\end{array}\right]$$
2. $$\left[\begin{array}{cc}3& 40\\ 42& 8\end{array}\right]$$
3. $$\left[\begin{array}{cc}43& 27\\ 34& 50\end{array}\right]$$
4. $$\left[\begin{array}{cc}38& 32\\ 28& 56\end{array}\right]$$

Q. If A and B are real symmetric matrices of order n then which of the following is true.

1. $A{A}^T=I$
2. $A=A^{-1}$
3. $AB=BA$
4. $(AB{)}^T=B^T{A}^T$

Q.

What is the Matrix Theory?

Q. The product $\left[P\right][Q{]}^T$ of the following two matrices [P] and [Q] is

$\left[P\right]=\left[\begin{array}{cc}2& 3\\ 4& 5\end{array}\right]$ ; $\left[Q\right]=\left[\begin{array}{cc}4& 8\\ 9& 2\end{array}\right]$

1. $\left[\begin{array}{cc}32& 24\\ 56& 46\end{array}\right]$
2. $\left[\begin{array}{cc}46& 56\\ 24& 32\end{array}\right]$
3. $\left[\begin{array}{cc}35& 22\\ 61& 42\end{array}\right]$
4. $\left[\begin{array}{cc}32& 56\\ 24& 46\end{array}\right]$

Q. If a matrix $A=\left[\begin{array}{cc}2& 4\\ 1& 3\end{array}\right]$ and matrix $B=\left[\begin{array}{cc}4& 6\\ 5& 9\end{array}\right]$, then the transpose of product of these two matrices I.e., $(AB{)}^T$ is equal to

1. $\left[\begin{array}{cc}28& 19\\ 34& 47\end{array}\right]$
2. $\left[\begin{array}{cc}19& 34\\ 47& 28\end{array}\right]$
3. $\left[\begin{array}{cc}48& 33\\ 28& 19\end{array}\right]$
4. $\left[\begin{array}{cc}28& 19\\ 48& 33\end{array}\right]$

Q. Given the matrices the product $B^{T}AB$ is _______
$A=\left[\begin{array}{ccc}1& 2& 3\\ 1& 2& 4\\ 6& 2& 1\end{array}\right]$ and $B=\left[\begin{array}{c}2\\ 4\\ -2\end{array}\right]$

1. -20

Q. Given matrix L=$\left[\begin{array}{cc}2& 1\\ 3& 2\\ 4& 5\end{array}\right]andM=\left[\begin{array}{cc}3& 2\\ 0& 1\end{array}\right]thenL\times Mis$

1. $\left[\begin{array}{cc}8& 1\\ 13& 2\\ 22& 5\end{array}\right]$
2. $\left[\begin{array}{cc}6& 5\\ 9& 8\\ 12& 13\end{array}\right]$
   
3. $\left[\begin{array}{cc}1& 8\\ 2& 13\\ 5& 22\end{array}\right]$
   
4. $\left[\begin{array}{cc}6& 2\\ 9& 4\\ 0& 5\end{array}\right]$
   

Q. The product $\left[P\right][Q{]}^T$ of the following two matrices [P] and [Q] is

$\left[P\right]=\left[\begin{array}{cc}2& 3\\ 4& 5\end{array}\right]$ ; $\left[Q\right]=\left[\begin{array}{cc}4& 8\\ 9& 2\end{array}\right]$

1. $\left[\begin{array}{cc}32& 24\\ 56& 46\end{array}\right]$
2. $\left[\begin{array}{cc}46& 56\\ 24& 32\end{array}\right]$
3. $\left[\begin{array}{cc}35& 22\\ 61& 42\end{array}\right]$
4. $\left[\begin{array}{cc}32& 56\\ 24& 46\end{array}\right]$

Q. If A and B are real symmetric matrices of order n then which of the following is true.

1. $A{A}^T=I$
2. $A=A^{-1}$
3. $AB=BA$
4. $(AB{)}^T=B^T{A}^T$

Q. If matrix A is $m\times n$ and B is $n\times p$, the number of multipication operations and addition operations needed to calculate the matrx AB, respectively, are:

1. $m{n}^{2}p,mpn$
2. mpn, (n-1)
3. $mpn,mp(n-1)$
4. $m{n}^{2}p;(m+p)n$