defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Matrices Adjoint and Inverse of a Square Matrix
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
1
\(\left[ {\begin{array}{*{20}{c}} {{a^{ - 1}}}&0&0\\ 0&{{b^{ - 1}}}&0\\ 0&0&{{c^{ - 1}}} \end{array}} \right]\)
2
\(\frac{1}{{abc}}\left[ {\begin{array}{*{20}{c}} {{a^{ - 1}}}&0&0\\ 0&{{b^{ - 1}}}&0\\ 0&0&{{c^{ - 1}}} \end{array}} \right]\)
3
\(\frac{1}{{abc}}\left[ {\begin{array}{*{20}{c}} 1&0&0\\ 0&1&0\\ 0&0&1 \end{array}} \right]\)
4
\(\frac{1}{{abc}}\left[ {\begin{array}{*{20}{c}} a&0&0\\ 0&b&0\\ 0&0&c \end{array}} \right]\)