Question

Let $a, b \in R \rightarrow\{0\}$, and $I_{2}$ be the identity matrix of order $2$ Then the rank of the (block) matrix $\begin{bmatrix}a I_{2} & b I_{2} \\ a I_{2} & b I_{2}\end{bmatrix}$ is

• A. 2
• B. 1
• C. 4
• D. 3

Answer 1

Answer: (A)

Since $a, b \in R-\{0\}$ and $I_{2}$ is a identify matrix of order $2$.
Then the block matrix $\begin{bmatrix}a I_{2} & b I_{2} \\ a I_{2} & b I_{2}\end{bmatrix}$ is a non-singular