If A = [ beginmatrix2&0&0 2&2&0 2&2&2 endmatrix], then adj (adj A) is equal to

Question

If A = [ beginmatrix2&0&0 2&2&0 2&2&2 endmatrix], then adj (adj A) is equal to (A) 8 [ beginmatrix1&0&0 1&1&0 1&1&1 endmatrix] (B) 12 [ beginmatrix1&0&0 1&1&0 1&1&1 endmatrix] (C) 16 [ beginmatrix1&0&0 1&1&0 1&1&1 endmatrix] (D) none of these

Tardigrade Admin · Accepted Answer

We have, A =[ beginmatrix2&0&0 2&2&0 2&2&2 endmatrix] ∴ adj A =[ beginmatrix4&0&0 -4&4&0 0&-4&4 endmatrix] ∴ adj (adjA) =[ beginmatrix16&0&0 16&16&0 16&16&16 endmatrix]=16 [ beginmatrix1&0&0 1&1&0 1&1&1 endmatrix]

Q. If $A = ⎣ ⎡ 222022002 ⎦ ⎤$ , then adj (adj A) is equal to

$8 ⎣ ⎡ 111011001 ⎦ ⎤$

$12 ⎣ ⎡ 111011001 ⎦ ⎤$

$16 ⎣ ⎡ 111011001 ⎦ ⎤$

none of these

We have, $A = ⎣ ⎡ 222022002 ⎦ ⎤$

$∴ a d j A = ⎣ ⎡ 4 - 4 0 04 - 4 004 ⎦ ⎤$

$∴ a d j (a d j A) = ⎣ ⎡ 161616016160016 ⎦ ⎤ = 16 ⎣ ⎡ 111011001 ⎦ ⎤$

Q. If A=⎣⎡​222​022​002​⎦⎤​, then adj (adj A) is equal to

8⎣⎡​111​011​001​⎦⎤​

12⎣⎡​111​011​001​⎦⎤​

16⎣⎡​111​011​001​⎦⎤​