matrix multiplication

Consider two matrices A = $\begin{bmatrix} 2 & 1 & 4 \\ 1 & 0 & 3 \end{bmatrix}$ and B = $\begin{bmatrix} -1 & 0 \\ 2 & 3 \\ 1 & 4 \end{bmatrix}$. The determinant of the matrix AB...

Consider two matrices $A = \begin{bmatrix}2 & 1 & 4 \\ 1 & 0 & 3\end{bmatrix}$ and $B = \begin{bmatrix}-1 & 0 \\ 2 & 3 \\ 1 & 4 \end{bmatrix}$. The determinant of the matrix $AB$ i...

If $P = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $Q = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}$ then $Q^T P^T$ is

If $A = \begin{bmatrix} 1 & 5 \\ 6 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & 7 \\ 8 & 4 \end{bmatrix}$, $AB^T$ is equal to

Given the matrices $$J = \left[ {\matrix{ 3 & 2 & 1 \cr 2 & 4 & 2 \cr 1 & 2 & 6 \cr } } \right]$$ and $$K = \left[ {\matrix{ 1 \cr 2 \cr { - 1} \cr } } \right],\,\,$$ the product $...

What is the minimum number of multiplications involved in computing the matrix product $$PQR?$$ Matrix $$P$$ has $$4$$ rows and $$2$$ columns, matrix $$Q$$ has $$2$$ rows and $$4$$...

Consider the matrices $$\,{X_{4x3,}}\,\,{Y_{4x3}}$$ $$\,\,{P_{2x3}}.$$ The order of $$\,{\left[ {P{{\left( {{X^T}Y} \right)}^{ - 1}}{P^T}} \right]^T}$$ will be

Real matrices $$\,\,{\left[ A \right]_{3x1,}}$$ $$\,\,{\left[ B \right]_{3x3,}}$$ $$\,\,{\left[ C \right]_{3x5,}}$$ $$\,\,{\left[ D \right]_{5x3,}}$$ $$\,\,{\left[ E \right]_{5x5,}...

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

If $$A$$ and $$B$$ are two matrices and $$AB$$ exists then $$BA$$ exists,