If A is a square matrix of order 3 and entries of A are positive integers then | A | is

Question

If A is a square matrix of order 3 and entries of A are positive integers then | A | is (A) different from zero (B) 0 (C) positive (D) an arbitrary integer

Tardigrade Admin · Accepted Answer

|A| = |5&2 3&1| = 5 - 6 = - 1 Adj A = beginpmatrix1&-2 -3&5 endpmatrix if A = beginpmatrix5&2 3&1 endpmatrix ∴ A-1 = beginpmatrix-1&2 3&-5 endpmatrix

Q. If A is a square matrix of order 3 and entries of A are positive integers then | A | is

different from zero

0

positive

an arbitrary integer

$∣ A ∣ = ∣ ∣ 5321 ∣ ∣ = 5 - 6 = - 1$
Adj A = $(1 - 3 - 2 5)$ if A = $(5321)$
$∴$ $A^{- 1} = (- 1 3 2 - 5)$

Q. If A is a square matrix of order 3 and entries of A are positive integers then | A | is

different from zero

0

positive

an arbitrary integer

∣A∣=∣∣​53​21​∣∣​=5−6=−1 Adj A = (1−3​−25​) if A = (53​21​) ∴ A−1=(−13​2−5​)

$∣ A ∣ = ∣ ∣ 5321 ∣ ∣ = 5 - 6 = - 1$
Adj A = $(1 - 3 - 2 5)$ if A = $(5321)$
$∴$ $A^{- 1} = (- 1 3 2 - 5)$