If a, b, c are non-zero real numbers, then the inverse of the matrix $A = \left[ {\begin{array}{*{20}{c}} a&0&0\ 0&b&0\ 0&0&c \end{array}} \right]$ is equal to

Question

If a, b, c are non-zero real numbers, then the inverse of the matrix $A = \left[ {\begin{array}{*{20}{c}} a&0&0\ 0&b&0\ 0&0&c \end{array}} \right]$ is equal to

TuteeHUB · Accepted Answer

$\frac{1}{{abc}}\left[ {\begin{array}{*{20}{c}} {{a^{ - 1}}}&0&0\ 0&{{b^{ - 1}}}&0\ 0&0&{{c^{ - 1}}} \end{array}} \right]$

TuteeHUB · Answer

$\left[ {\begin{array}{*{20}{c}} {{a^{ - 1}}}&0&0\ 0&{{b^{ - 1}}}&0\ 0&0&{{c^{ - 1}}} \end{array}} \right]$

TuteeHUB · Answer

$\frac{1}{{abc}}\left[ {\begin{array}{*{20}{c}} 1&0&0\ 0&1&0\ 0&0&1 \end{array}} \right]$

TuteeHUB · Answer

$\frac{1}{{abc}}\left[ {\begin{array}{*{20}{c}} a&0&0\ 0&b&0\ 0&0&c \end{array}} \right]$

1.	If a, b, c are non-zero real numbers, then the inverse of the matrix \(A = \left[ {\begin{array}{*{20}{c}} a&0&0\\ 0&b&0\\ 0&0&c \end{array}} \right]\) is equal to
A.	\(\left[ {\begin{array}{*{20}{c}} {{a^{ - 1}}}&0&0\\ 0&{{b^{ - 1}}}&0\\ 0&0&{{c^{ - 1}}} \end{array}} \right]\)
B.	\(\frac{1}{{abc}}\left[ {\begin{array}{*{20}{c}} {{a^{ - 1}}}&0&0\\ 0&{{b^{ - 1}}}&0\\ 0&0&{{c^{ - 1}}} \end{array}} \right]\)
C.	\(\frac{1}{{abc}}\left[ {\begin{array}{*{20}{c}} 1&0&0\\ 0&1&0\\ 0&0&1 \end{array}} \right]\)
D.	\(\frac{1}{{abc}}\left[ {\begin{array}{*{20}{c}} a&0&0\\ 0&b&0\\ 0&0&c \end{array}} \right]\)
Answer» B. \(\frac{1}{{abc}}\left[ {\begin{array}{*{20}{c}} {{a^{ - 1}}}&0&0\\ 0&{{b^{ - 1}}}&0\\ 0&0&{{c^{ - 1}}} \end{array}} \right]\)

If a, b, c are non-zero real numbers, then the inverse of the matrix \(A = \left[ {\begin{array}{*{20}{c}} a&0&0\\ 0&b&0\\ 0&0&c \end{array}} \right]\) is equal to

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