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Mathematics
Inverse of matrix
There are two possible values of $A$ in the Solution of the Matrix Equation
${\left[ {\begin{array}{*{20}{c}} {2A + 1}&{ - 5} \\ { - 4}&A \end{array}} \right]^{ - 1}}\left[ {\begin{array}{*{20}{c}} {A - 5}&B \\ {2A - 2}&C \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {14}&D \\ E&F \end{array}} \right]$ Where $A,B,C,D,E,F$ are Real Numbers. The absolute value of the difference between these two solutions is
$a)\dfrac{8}{3} \\ b)\dfrac{{11}}{3} \\ c)\dfrac{1}{3} \\ d)\dfrac{{19}}{3} \\$
Mathematics
Inverse of matrix
Using elementary transformation, find the inverse of the matrix $\left[ {\begin{array}{*{20}{c}} 3&{10} \\ 2&7 \end{array}} \right]$.

Mathematics
Inverse of matrix
If ${{\text{A}}^2} - {\text{A}} + {\text{I}} = 0$, then the inverse of ${\text{A}}$ is:
A) ${\text{A - I}}$
B) ${\text{I - A}}$
C) ${\text{A + I}}$
D) ${\text{A}}$

Mathematics
Inverse of matrix
Let two matrices are given as A $=\left( \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \\ \end{matrix} \right)$ and 10B $=\left( \begin{matrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \\ \end{matrix} \right)$ . If B is the inverse of A, then find the value of $\alpha$ .

Mathematics
Inverse of matrix
Can we say that a zero matrix is invertible?

Mathematics
Inverse of matrix
The inverse of symmetric matrix is
A. Symmetric
B. Skew-Symmetric
C. Diagonal matrix
D. None of these
Mathematics
Inverse of matrix
Find the inverse of $A=\left[ \begin{matrix} \cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right]$
(i) By elementary row transformation
(ii) By elementary column transformation
Mathematics
Inverse of matrix
If $AX=B$, where $A=\left[ \begin{matrix} 3 & 1 \\ -1 & 2 \\ \end{matrix} \right]$, $B=\left[ \begin{matrix} 7 & 3 \\ 0 & 6 \\ \end{matrix} \right]$. Then $X=$?
A. $\left[ \begin{matrix} 1 & 0 \\ 2 & 3 \\ \end{matrix} \right]$
B. $\left[ \begin{matrix} 0 & 3 \\ 1 & 2 \\ \end{matrix} \right]$
C. $\left[ \begin{matrix} 3 & 2 \\ 0 & 1 \\ \end{matrix} \right]$
D. $\left[ \begin{matrix} 2 & 0 \\ 1 & 3 \\ \end{matrix} \right]$

Mathematics
Inverse of matrix
How do you find the inverse of $A=\left[ \begin{matrix} 3 & 5 \\ 2 & 4 \\ \end{matrix} \right]$ ?

Mathematics
Inverse of matrix
Let $A=\left[ \begin{matrix} x+\lambda & x & x \\ x & x+\lambda & x \\ x & x & x+\lambda \\ \end{matrix} \right]$, then ${{A}^{-1}}$ exist if

Mathematics
Inverse of matrix
How do find the inverse of $A = ((1,1,2)\,(2,2,2)\,(2,1,1))$ ?
Mathematics
Inverse of matrix
If A and B are two square matrices such that $B = - {A^{ - 1}}BA$ , then ${\left( {A + B} \right)^2}$ is equal to ?

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