MHT CET · Maths · Matrices
If \(A=\left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right]_{3 \times 3}\), then \(A^{-1}=\)
- A \(A\)
- B \(\mathrm{A}^2\)
- C \(\mathrm{A}^3\)
- D \(\mathrm{A}^4\)
Answer & Solution
Correct Answer
(C) \(\mathrm{A}^3\)
Step-by-step Solution
Detailed explanation
\( \det(A) = 3((-3)(1)-(4)(-1)) - (-3)((2)(1)-(4)(0)) + 4((2)(-1)-(-3)(0)) = 3(1) + 3(2) + 4(-2) = 1 \) \( \text{Cofactor}(A) = \left[ \begin{array}{ccc} 1 & -2 & -2 \\ -1 & 3 & 3 \\ 0 & -4 & -3 \end{array} \right] \)
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