Home
Class 12
MATHS
Let A be a square matrix all of whose...

Let A be a square matrix all of whose entries are integers. Then which one of the following is true? (1) If `d e t A""=+-1,""t h e n""A^(1)` exists but all its entries are not necessarily integers (2) If `d e t A!=""+-1,""t h e n""A^(1)` exists and all its entries are non-integers (3) If `d e t A""=+-1,""t h e n""A^(1)` exists and all its entries are integers (4) If `d e t A""=+-1,""t h e n""A^(1)` need not exist

Text Solution

Verified by Experts

`[A]=` integer
`[A]_C=`integer
`A^-1 = ([A]_C)/(det|A|)`
`A^-1=`integer
option 3 is correct
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    JEE MAINS PREVIOUS YEAR|Exercise All Questions|6 Videos

  • PARABOLA

    JEE MAINS PREVIOUS YEAR|Exercise All Questions|9 Videos

Similar Questions

Explore conceptually related problems

Differentiate the following w.r.t. x : 1/3e^(x)-5e

For the function f(x)=(e^(x)+1)/(e^(x)-1) if n(d) denotes the number of integers which are not in its domain and n(r) denotes the number of integers which are not in its range,then n(d)+n(r) is equal to

If a , b , c are all positive and are p t h ,q t ha n dr t h terms of a G.P., then that =|loga p1logb q1logc r1|=0

Which of the following statements is/are true about square matrix A or order n?(-A)^(-1) is equal to -A^(-1) when n is odd only If A^(n)-O, then I+A+A^(2)+...+A^(n-1)=(I-A)^(-1) If A is skew-symmetric matrix of odd order,then its inverse does not exist.(A^(T))^(-1)=(A^(-1))^(T) holds always.

The value of int_(-1)^(1)x^(2)e^([x^(3)])dx , where [t] denotes the greatest integer le t , is :

If n is a whole number such that n+n=n ,\ t h e n\ n=? (a) 1 (b) 2 (c) 3 (d) none of these

int_e^(e(-1)) 1/(t(t+1)) dt