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Question
If $$\left[ {\matrix{ 1 & 1 \cr 0 & 1 \cr } } \right]\left[ {\matrix{ 1 & 2 \cr 0 & 1 \cr } } \right]$$\left[ {\matrix{ 1 & 3 \cr 0 & 1 \cr } } \right]$....$\left[ {\matrix{ 1 & {n - 1} \cr 0 & 1 \cr } } \right] = \left[ {\matrix{ 1 & {78} \cr 0 & 1 \cr } } \right]$$,

then the inverse of $$\left[ {\matrix{ 1 & n \cr 0 & 1 \cr } } \right]$$ is
$$\left[ {\matrix{ 1 & { 0} \cr {12} & 1 \cr } } \right]$$
$$\left[ {\matrix{ 1 & { 0} \cr {13} & 1 \cr } } \right]$$
$$\left[ {\matrix{ 1 & { - 13} \cr 0 & 1 \cr } } \right]$$
$$\left[ {\matrix{ 1 & { - 12} \cr 0 & 1 \cr } } \right]$$

Solution

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