AP EAMCET · Maths · Matrices
Let \(a, b \in \mathbf{R}-\{0\}\), and \(I_2\) be the identity matrix of order 2. Then the rank of the (block) matrix \(\left[\begin{array}{ll}a I_2 & b_2 \\ a I_2 & b I_2\end{array}\right]\) is
- A 2
- B 1
- C 4
- D 3
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
Since \(a, b \in \mathbf{R}-\{0\}\) and \(I_2\) is a identify matrix of order 2 . Then the block matrix \(\left[\begin{array}{ll}a I_2 & b I_2 \\ a I_2 & b I_2\end{array}\right]\) is a non-singular matrix, so the rank of the given block matrix is 2.
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