If A is a non-singular matrix, then

Question

If A is a non-singular matrix, then

If A is a non-singular matrix, then
A. `A^(-1)` is a non-singular matrix, then
B. `A^(-1)`is skew-symmetric if A is symmetric
C. `abs(A^-1) = abs(A)`
D. `abs(A^-1) = abs(A)^(-1)`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Related Questions

Prove that the inverse of `[[A,O],[B,C]]` is `[[A^(-1),O],[-C^(-1)BA^(-1),C^(-1)]]` , where A, Care non-singular matrices and O is null matrix and fin

2 Answers 4 Views

If A is non-singular and `(A-2I) (A-4I) = O`, then `1/6 A + 4/3 A^(-1)` is equal to

2 Answers 4 Views

Suppose A and B be two ono-singular matrices such that `AB= BA^(m), B^(n) = I and A^(p) = I `, where `I` is an identity matrix. The relation between m

2 Answers 4 Views

Suppose A and B be two ono-singular matrices such that `AB= BA^(m), B^(n) = I and A^(p) = I `, where `I` is an identity matrix. Which of the following

2 Answers 5 Views

If A is symmetric and B skew- symmetric matrix and `A + B ` is non-singular and `C= (A+B) ^(-1) (A-B)` , `C^(T)(A+B)C` equals to

2 Answers 5 Views

If A is a symmetric and B skew symmetric matrix and `(A+ B)` is non-singular and `C = (A+B)^-1 (A-B)`, then prove that

2 Answers 4 Views

If A is symmetric and B skew- symmetric matrix and `A + B ` is non-singular and `C= (A+B) ^(-1) (A-B)` `C^(T) AC` equals to

2 Answers 4 Views

If s is a real skew-symmetric matrix, the show that `I-S` is non-singular and matrix `A= (I+S) (I-S) ^(-1) = (I-S) ^(-1) (I+S) ` is orthogonal.

2 Answers 4 Views

If A non-singular matrix such that `(A-2l)(A-4l)=0` then A=`8A^(-1)=` . .

2 Answers 4 Views

More of nouns having singular and plural alike. Singular : 1. news 2. aircraft 3. species 4. darts

2 Answers 4 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - A::D
`because abs(A) ne 0 rArr A^(-1) `
is also symmetric, if A is symmetric
and `abs(A^(-1)) = 1/abs(A) = abs(A) ^(-1)`

4 views Answered 2023-02-05 15:29