If $\begin{bmatrix$}[r] 3 & 4 \ 2 & 5 \end{bmatrix} = \begin{bmatrix}[r] a & b \ c & d \end{bmatrix} \begin{bmatrix}[r] 1 & 0 \ 0 & 1 \end{bmatrix}, write down the values of a, b, c and d.

Given,

$\begin{bmatrix$}[r] 3 & 4 \ 2 & 5 \end{bmatrix} = \begin{bmatrix}[r] a & b \ c & d \end{bmatrix} \begin{bmatrix}[r] 1 & 0 \ 0 & 1 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 3 & 4 \ 2 & 5 \end{bmatrix} = \begin{bmatrix}[r] a \times 1 + b \times 0 & a \times 0 + b \times 1 \ c \times 1 + d \times 0 & c \times 0 + d \times 1 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix}[r] 3 & 4 \ 2 & 5 \end{bmatrix} = \begin{bmatrix}[r] a & b \ c & d \end{bmatrix}

By definition of equality of matrices,

⇒ a = 3, b = 4, c = 2 and d = 5

Hence, the value of a = 3, b = 4, c = 2 and d = 5.