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

Question

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, 2, 1, 4, 3

MARKS App · Accepted Answer

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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