If A=0121233a1 and A−1=12-1212-43c52-3212 then

we must have AA−1=I(3, 1)th entry of AA−1=0=(1,3)th entry of AA−1 ⇒3×12+a×(−4)+1×52=0 =0×12+1×c+2×12=0⇒−4a+4=0 and c+ 1 = 0⇒ a = 1 and c = -1

If A=0121233a1 and A−1=12-1212-43c52-3212 then

we must have AA−1=I(3, 1)th entry of AA−1=0=(1,3)th entry of AA−1 ⇒3×12+a×(−4)+1×52=0 =0×12+1×c+2×12=0⇒−4a+4=0 and c+ 1 = 0⇒ a = 1 and c = -1

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If $A = [\begin{matrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1 \end{matrix}]$ and $A^{- 1} = [\begin{matrix} \frac{1}{2} & - \frac{1}{2} & \frac{1}{2} \\ - 4 & 3 & c \\ \frac{5}{2} & \frac{- 3}{2} & \frac{1}{2} \end{matrix}]$ then

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$a = 2, c = \frac{1}{2}$

$a = 1, c = - 1$

$a = - 1, c = 1$

$a = \frac{1}{2}, c = \frac{1}{2}$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

we must have $A A^{- 1} = I$
(3, 1)th entry of $A A^{- 1} = 0 = (1, 3) t h$ entry of $A A^{- 1}$
$\Rightarrow 3 \times \frac{1}{2} + a \times (- 4) + 1 \times \frac{5}{2} = 0$
$= 0 \times \frac{1}{2} + 1 \times c + 2 \times \frac{1}{2} = 0$
$\Rightarrow - 4 a + 4 = 0$ and c+ 1 = 0
$\Rightarrow$ a = 1 and c = -1