1. ## Help need

Hi can someone please help me the following proofs. Look at the picture. Thanks i really appriate it

2. Originally Posted by maths_123
Hi can someone please help me the following proofs. Look at the picture. Thanks i really appriate it
For (i) put $B=-A$.

For (ii) consider $A^{-1}(\alpha A)$

For (iii) consider $A^{-1}(AB)=A^{-1}(AC)$

For (v) (vi) and (vii) think about the definition of determinants in terms of sums of products of elements with signs depending on which elements appear in the product.

CB

3. We know that
det[kA]=k^n *det[A] ...........for nxn matrix A

(v) is false
for 2x2 marix A
det[-A]=(-1)^2 det[A]
det[-A]= det[A]

(vi) is true
for 3x3 martix A
det[-A]=(-1)^3 *det[A]
det[-A]=- det[A]

(vii) is false
for 3x3 martix A
det[αA]=α^3 *det[A]