You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Singular and Non Singualar Matrices

Let A=[ a b...

Question

Let $A = [\begin{matrix} a & b c & d \end{matrix}]$ be a $2 \times 2$ matrix, where a, b, c and d take the values $0$ or $1$ only. The number of such matrices which have inverses is?

8

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

7

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $8$
$A^{- 1} = \frac{a d j A}{| A |}$
so $| A | \neq 0 a d - b c \neq 0$
for $a d - b c \neq 0$
either $a d = 1, b c = 0$ or $a d = 0, b c = 1$
$a d = 1, b c = 0$ can be chosen in 4 ways
similarly $a d = 0, b c = 1$ can be chosen in 4 ways
so number of matrices formed $= 4 + 4 = 8$

Suggest Corrections

Similar questions

Q. Let

A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 7 0 & 1 & 0 1 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦

and

B = ⎡ ⎢ ⎣ \begin{matrix} - x & 14 x & 7 x 0 & 1 & 0 x & - 4 x & - 2 x \end{matrix} ⎤ ⎥ ⎦

are two matrices such that

A B = (A B)^{- 1}

and

A B \neq I

(where

I

is an identity matrix of order

3 \times 3

).
Find the value of

T r . (A B + (A B)^{2} + (A B)^{3} + . . . + (A B)^{100})

where

T r . (A)

denotes the trace of matrix

A

Let $A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]$ and $B = [\begin{matrix} a & b c & d \end{matrix}]$ are two matrices such that AB = BA and $c \neq 0$ , then value of $\frac{a - d}{3 b - c}$ is :

Let $A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]$ and $B = A = [\begin{matrix} a & b c & d \end{matrix}]$ are two matrices such that AB = BA and $c \neq 0$ , then value of $\frac{a - d}{3 b - c}$ is :

Q. Let

A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]

and

B = [\begin{matrix} a & b c & d \end{matrix}]

be two matrices such that they are commutative and

c \neq 3 b

. Then, find the value of

(d - a) / (3 b - c)

Q. Matrices A and B will be inverse of each other only if A. AB = BA C. AB = 0, BA = I B. AB = BA = 0 D. AB = BA = I

Join BYJU'S Learning Program

Let A=[abcd] be a 2×2 matrix, where a, b, c and d take the values 0 or 1 only. The number of such matrices which have inverses is?

The correct option is D 8A−1=adjA|A|so |A|≠0ad−bc≠0for ad−bc≠0 either ad=1,bc=0 or ad=0,bc=1ad=1,bc=0 can be chosen in 4 ways similarly ad=0,bc=1 can be chosen in 4 waysso number of matrices formed=4+4=8

Let $A = [\begin{matrix} a & b c & d \end{matrix}]$ be a $2 \times 2$ matrix, where a, b, c and d take the values $0$ or $1$ only. The number of such matrices which have inverses is?