Given below are two statements. STATEMENT - 1: If a, b, c, d are real numbers and A= […
Mathematics · JEE Main · NTA Exams — Matrices and Determinants
STATEMENT - 1: If a, b, c, d are real numbers and \(A=\left[\begin{array}{ll} a & b \\ c & d \end{array}\right]\) and \(A^{3}=0\), then \(A^{2}=0\).
STATEMENT - 2: For matrix \(\mathbf{A}=\left[\begin{array}{ll} \mathbf{a} & \mathbf{b} \\ \mathbf{c} & \mathbf{d} \end{array}\right],\) we have \(A^{2}-(a+d) A+(a d-b c) I=0\).
In the light of the above statements, choose the correct answer from the options given below:
- Both the statements are true and Statement - 2 is the correct explanation of Statement - 1
- Both the statements are true but Statement - 2 is not the correct explanation of Statement - 1
- Statement - 1 is true and Statement - 2 is false
- Statement - 1 is false and Statement - 2 is true
Answer
(A) Both the statements are true and Statement - 2 is the correct explanation of Statement - 1
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