Question

If A= [(5,2) (2,1)] then (adj A).A is :

a) I
b)A
c)-A
d)A^2​

Answer 1

a) I.

Step-by-step explanation:

• Given that $A=\left[\begin{array}{cc}5&2&\\2&1\\\end{array}\right]$

• To prove Adj (A) = ?

• Order of A is 2  × 2

• To find AdjA in 2 × 2 matrix

       $if A =\left[\begin{array}{cc}a&b&\\c&d\\\end{array}\right]$     then   $AdjA(A)=\left[\begin{array}{cc}d&-b&\\-c&a\\\end{array}\right]$

• $A=\left[\begin{array}{cc}5&2&\\2&1\\\end{array}\right]$      then    $AdjA(A)=\left[\begin{array}{cc}1&-2&\\-2&5\\\end{array}\right]$

• $AdjA(A)= \left[\begin{array}{cc}1&-2&\\-2&5\\\end{array}\right]$ $\left[\begin{array}{cc}5&2&\\2&1\\\end{array}\right]$

• By using matrix multiplication technique.

• $\left[\begin{array}{cc}5-4&2-2&\\-10+10&-4+5\\\end{array}\right]$

• $\left[\begin{array}{cc}1&0&\\0&1\\\end{array}\right]= I$

I is the identity matrix of order 2.

Answer 2

Answer

The steps for your Answer are there in above pic

pls do refer the pic for step by step answer

• Thank you