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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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