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Minor and Cofactor of a Matrix

If A=[aij] is...

Question

If $A = [a_{i j}]$ is a $2 \times 2$ matrix. Then which of the following statements is/are always true?

Sum of minors of elements of

A

is equal to sum of its elements

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Sum of minors of elements of

A

is equal to twice the sum of its elements

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Product of minors of elements of

A

is equal to the product of its elements

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Product of minors of elements of

A

is equal to the product of square of its elements

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Solution

The correct option is C Product of minors of elements of $A$ is equal to the product of its elements
Let $A = [\begin{matrix} a & b c & d \end{matrix}]$
Then,
$M_{11} = d, M_{12} = c, M_{21} = b, M_{22} = a$
So, sum of minors of elements of $A = a + b + c + d$
Product of minors of elements of $A = a b c d$

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If A=[aij] is a 2×2 matrix. Then which of the following statements is/are always true?

The correct option is C Product of minors of elements of A is equal to the product of its elements Let A=[abcd] Then, M11=d,M12=c,M21=b,M22=a So, sum of minors of elements of A=a+b+c+d Product of minors of elements of A=abcd

If $A = [a_{i j}]$ is a $2 \times 2$ matrix. Then which of the following statements is/are always true?