Question

 A, B and C are three square matrices each of order 3; the order of matrix CA + B² is ______.

विकल्प

• 3 × 1

• 3 × 3

• 1 × 3

• 2 × 3

Answer 1

 A, B and C are three square matrices each of order 3; the order of matrix CA + B² is 3 × 3.

Explanation:

Let resultant matrix of CA be R.

C_{3 × 3} × A_{3 × 3} = R_{m × n}

We know that,

For matrix multiplication:

No. of columns in C must be equal to the number of rows in A.

Resultant matrix order = No. of rows in C × No. of columns in A.

∴ m = 3 and n = 3.

∴ Order of matrix R will be 3 × 3.

Let resultant matrix of B² be S.

B_{3 × 3} × B_{3 × 3} = S_{g × h}

Resultant matrix order = No. of rows in B × No. of columns in B.

∴ g = 3 and h = 3.

∴ Order of matrix S will be 3 × 3.

⇒ CA + B²

⇒ R + S

Addition of matrix possible between matrix of same order and same is the order of resultant matrix.

Hence, resultant matrix's order = 3 × 3.