Let a, b in R-{0},and I_2 be the identity mat | vedclass

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(A) Let $M = \begin{bmatrix} a I_2 & b I_2 \ a I_2 & b I_2 \end{bmatrix}$. Since $a, b \in R-\{0\}$,we can perform row operations on the block matrix

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(A) Let $M = \begin{bmatrix} a I_2 & b I_2 \ a I_2 & b I_2 \end{bmatrix}$. Since $a, b \in R-\{0\}$,we can perform row operations on the block matrix. Subtracting the first block row from the second block row,we get: $M \sim \begin{bmatrix} a I_2 & b I_2 \ a I_2 - a I_2 & b I_2 - b I_2 \end{bmatrix} = \begin{bmatrix} a I_2 & b I_2 \ 0 & 0 \end{bmatrix}$. The rank of a matrix is the number of linearly independent rows. Here,the first block row is $\begin{bmatrix} a I_2 & b I_2 \end{bmatrix}$,which is non-zero because $a 
eq 0$. The second block row is the zero matrix. Thus,the rank of the matrix is equal to the rank of $a I_2$,which is $2$.

Let $a, b \in R-\{0\}$,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

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