matrix multiplication

Let $P = \begin{bmatrix} 2 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ and let $I$ be the identity matrix. Then $P^2$ is equal to

Let $P=\left[\begin{array}{ccc}2 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1\end{array}\right]$ and let $I$ be the identity matrix. Then $P^2$ is equal to

$$A = \left[ {\matrix{ p & q \cr r & s \cr } } \right];B = \left[ {\matrix{ {{p^2} + {q^2}} & {pr + qs} \cr {pr + qs} & {{r^2} + {s^2}} \cr } } \right]$$ If the rank of matrix $$A$...

The matrix $$\left[ A \right] = \left[ {\matrix{ 2 & 1 \cr 4 & { - 1} \cr } } \right]$$ is decomposed into a product of lower triangular matrix $$\left[ L \right]$$ and an upper tr...

A three phase balanced star connected voltage source with frequency $$\omega \,\,rad/s$$ is connected to a star connected balanced load which is purely inductive. The instantaneous...

If the vector $$\left[ {\matrix{ 1 \cr 2 \cr { - 1} \cr } } \right]$$ is an eigen vector of $$A = \left[ {\matrix{ { - 2} & 2 & { - 3} \cr 2 & 1 & { - 6} \cr { - 1} & { - 2} & 0 \c...