If \(\begin{bmatrix}3&5\\1&2\end{bmatrix}\begin{bmatrix}a&b\\-1&c\end{bmatrix} = I\), where I is the identity matrix of order 2, then the value of \(a + b + c\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0
Multiplying row by column:
\( \displaystyle \begin{bmatrix}3a - 5&3b + 5c\\a - 2&b + 2c\end{bmatrix} = \begin{bmatrix}1&0\\0&1\end{bmatrix} \)
By equality of matrices, the first column gives
\(3a - 5 = 1\) and \(a - 2 = 0\), so \(a = 2\)
The second column gives
\(3b + 5c = 0\)
\(b + 2c = 1\)
Multiplying the second equation by 3 and subtracting the first:
\(c = 3\)
\(b = 1 - 2c = -5\)
Hence
\(a + b + c = 2 - 5 + 3 = 0\)