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Let M be a 2 x 2 symmetric matrix with i...

Let M be a 2 x 2 symmetric matrix with integer entries. Then M is invertible if
(a)The first column of M is the transpose of the second row of M
(b)The second row of Mis the transpose of the first olumn of M
(c) M is a diagonal matrix with non-zero entries in the main diagonal
(d)The product of entries in the main diagonal of Mis not the square of an integer

Text Solution

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`M->2*2` symmetric matrix
`M=M^T`
Suppose`M=[[a,b],[c,d]]`
`[[a,b],[c,d]]=[[a,c],[b,d]]`
`b=c`
Our matrix M=`[[a,b],[b,d]]`
`[[a],[b]]^T=[[b,d]]`
`[[a,b]]=[[b,d]]`
...
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