ISI2018-DCG-16

Question

Let $A=\begin{pmatrix} 1 & 1 & 0\\ 0 & a & b\\1 & 0 & 1 \end{pmatrix}$. Then $A^{-1}$ does not exist if $(a,b)$ is equal to

• A. $(1,-1)$
• B. $(1,0)$
• C. $(-1,-1)$
• D. $(0,1)$

Answer 1

A matrix is not invertible if it's determinant is $0.$

$|A|= 1(a-0)-1(0-b)= a+b$

Only Option A) satisfies

Answer 2

Option A satisfies the condition when we calculate the determinant we get a+b = 0 equation.