1.

A be a square matrix of order 2 with |A| ne 0 such that |A+|A|adj(A)|=0, where adj(A) is a adjoint of matrix A, then the value of |A-|A|adj(A)| is

Answer»

`1`
`2`
`3`
`4`

Solution :`(d)` Let `A=[{:(m,N),(p,q):}]`,`ADJ(a)=[{:(q,-n),(-p,m):}]`
Let `|A|=d=mq-np`
`|A+dadjA|=|{:(m+qd,n(1-d)),(p(1-d),q+md):}|=0`
`impliesmq+m^(2)d+q^(2)d+mqd^(2)-np+2npd-npd^(2)=0`
`IMPLIES(mq-np)+(mq0np)d^(2)+m^(2)d+q^(2)d+2mqd-2d^(2)=0`
`implies(d+d^(3)-2d^(2))+d(m^(2)+q^(2)+2mq)=0`
Now, `|A- d adj|A|=-(m+q)^(2)+4(mq-np)=4d=4`


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