Let’s look at what are minors & cofactor of a 2 × 2 & a 3 × 3 determinant

## For a 2 × 2 determinant

For

We have elements,

𝑎
_{
11
}
= 3

𝑎
_{
12
}
= 2

𝑎
_{
21
}
= 1

𝑎
_{
22
}
= 4

Minor will be

𝑀
_{
11
}
, 𝑀
_{
12
}
, 𝑀
_{
21
}
, 𝑀
_{
22
}

And cofactors will be

𝐴
_{
11
}
, 𝐴
_{
12
}
, 𝐴
_{
21
}
, 𝐴
_{
22
}

##
**
For a 3 × 3 matrix
**

Minor will be

*
M
_{
11
}
, M
_{
12
}
, M
_{
13
}
, M
_{
21
}
, M
_{
22
}
, M
_{
23
}
, M
_{
31
}
, M
_{
32
}
, M
_{
33
}
*

*
_{
}
*

Note :We can also calculate cofactors without calculating minors

Ifi+ j isodd,

A_{ ij }= −1 ×M_{ ij }

Ifi+ j iseven,

A_{ ij }=M_{ ij }

##
^{
But, why use cofactor?
}

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