Matrix A is given. Find appropriate identity matrices I m and I n such that I m A = A and AI n = A.
-$$A = \left[ \begin{array} { r r r r }
3 & 0 & 1 & 5 \
- 4 & 9 & - 1 & 7
\end{array} \right]$$
A) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right]$
B) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{array} \right]$
C) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right]$
D) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 1 \ 1 & 1 \end{array} \right]$

Question

Matrix A is given. Find appropriate identity matrices I m and I n such that I m A = A and AI n = A.
-$$A = \left[ \begin{array} { r r r r } 
3 & 0 & 1 & 5 \
- 4 & 9 & - 1 & 7
\end{array} \right]$$
A) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right]$
B) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{array} \right]$
C) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l l } 1 & 0 & 0 & 0 \ 0 & 1 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right]$
D) $\mathrm { I } _ { \mathrm { m } } = \left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right] , \mathrm { I } _ { \mathrm { n } } = \left[ \begin{array} { l l } 1 & 1 \ 1 & 1 \end{array} \right]$

Quizplus · Accepted Answer

Matrix $A$ is a $2 \times 4$ matrix. For $I_mA = A$, $I_m$ must be a $2 \times 2$ identity matrix to match the number of rows in $A$. For $AI_n = A$, $I_n$ must be a $4 \times 4$ identity matrix to match the number of columns in $A$.

Matrix a Is Given A=[3015−49−17]A = \left[ \begin{array} { r r r r } 3 & 0 & 1 & 5 \\- 4 & 9 & - 1 & 7\end{array} \right]A=[3−4​09​1−1​57​]

Matrix a Is Given $A = \left[ \begin{array} { r r r r } 3 & 0 & 1 & 5 \\- 4 & 9 & - 1 & 7\end{array} \right]$