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Recent questions tagged inverse

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ISI2014-DCG-70
For the matrices $A = \begin{pmatrix} a & a \\ 0 & a \end{pmatrix}$ and $B = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$, $(B^{-1}AB)^3$ ... ^3 & a^3 \end{pmatrix}$\begin{pmatrix} a^3 & 0 \\ -3a^3 & a^3 \end{pmatrix}$
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ISI2016-DCG-66
If $\sin(\sin^{-1}\frac{2}{5}+\cos^{-1}x)=1,$ then $x$ is$1$\frac{2}{5}$\frac{3}{5}$None of these
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ISI2018-DCG-16
Let $A=\begin{pmatrix} 1 & 1 & 0\\ 0 & a & b\\1 & 0 & 1 \end{pmatrix}$. Then $A^{-1}$ does not exist if $(a,b)$ is equal to$(1,-1)$(1,0)$(-1,-1)$(0,1)$
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ISI2018-DCG-20
The value of $\tan \left(\sin^{-1}\left(\frac{3}{5}\right)+\cot^{-1}\left(\frac{3}{2}\right)\right)$ is$\frac{1}{18}$\frac{11}{6}$\frac{13}{6}$\frac{17}{6}$
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